EXHIBIT 10.16

Confidential

COMMON STOCK PURCHASE AGREEMENT

This COMMON STOCK PURCHASE AGREEMENT (“Agreement”) is made as of July 23^rd, 2018 (the “Effective Date”), by and between SUTRO BIOPHARMA, INC., a Delaware corporation (the “Company”), and MERCK SHARP & DOHME CORP., a New Jersey corporation (the “Investor”).

RECITALS

WHEREAS, the Investor desires to purchase from the Company, and the Company desires to sell and issue to the Investor, up to $10.0 million of the common stock, par value $0.001 per share, of the Company (the “Common Stock”), in a private placement that would close concurrently with the Company’s initial public offering of Common Stock (the “IPO”) on the terms and subject to the conditions set forth in this Agreement (the “Financing”);

WHEREAS, the parties hereto have executed this Agreement on the Effective Date, which is prior to the effectiveness of the registration statement on Form S-1 to be filed by the Company with the Securities and Exchange Commission (the “SEC”) for the IPO;

WHEREAS, the closing of the Financing shall take place on the closing date of the closing of the IPO and at a price per share equal to the initial public offering price per share that the Common Stock is sold to the public in the IPO (the “IPO Price” and such date, the “IPO Closing Date”), as set forth on the cover of the final prospectus filed with the SEC; and

WHEREAS, in order to effect the IPO, the Company shall enter into an Underwriting Agreement (the “Underwriting Agreement”) with Cowen and Company, LLC and Piper Jaffray & Co., as representatives of the several underwriters named therein (the “Underwriters”).

AGREEMENT

NOW, THEREFORE, in consideration of the premises and the mutual covenants herein contained, and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereby agree as follows:

1. Purchase and Sale of Stock.

1.1 Sale and Issuance of Stock. The Company agrees to issue and sell to the Investor, and the Investor agrees to purchase from the Company, up to $10.0 million of Common Stock (or such lesser amount that is requested by the Company) (the “Investment Amount”) at the IPO Price pursuant to a private placement exempt from registration under the Securities Act of 1933, as amended (the “Securities Act”) in accordance with Rule 506 of Regulation D promulgated under the Securities Act; provided, however, that in the event the purchase by the Investor of the full Investment Amount would result in the Investor owning the Maximum Ownership Percentage or more of the outstanding Common Stock following consummation of the IPO and the Financing, then the Investment Amount shall be reduced to an amount that results in the ownership by the Investor of less than the Maximum Ownership Percentage of the outstanding Common Stock following consummation of the IPO and the Financing. The “Maximum Ownership Percentage” shall be 17.5% or such lesser percentage as advised in good faith and in writing by the Investor’s certified public accountants that would not require the Investor to include in its financial statements its portion of the Company’s financial results. The number of shares of Common Stock to be sold by the Company and purchased by the Investor hereunder (the “Shares”) shall equal the number of shares determined by dividing the Investment Amount (as adjusted as necessary pursuant to the proviso in the preceding sentence) by the IPO Price (rounded down to the nearest whole

share). Payment of the purchase price for the Shares (the “Purchase Price”) shall be made at the Closing (as defined below) by wire transfer of immediately available funds to the account specified in writing by the Company to the Investor, subject to the satisfaction of the conditions set forth in this Agreement. Payment of the Purchase Price for the Shares shall be made against delivery to the Investor of the Shares, which Shares shall be uncertificated and shall be registered in the name of the Investor on the books of the Company by the Company’s transfer agent.

1.2 Closing. The closing of the sale and purchase of the Shares (the “Closing”) will take place remotely via the exchange of documents and signatures after the satisfaction or waiver of each of the conditions set forth in Section 4 (other than those conditions that by their nature are to be satisfied at the Closing, but subject to the fulfillment or waiver of those conditions) on the IPO Closing Date.

2. Representations and Warranties of the Company. The Company hereby represents and warrants to the Investor that the following representations are true and correct as of the date hereof and as of the Closing (except to the extent any such representations and warranties expressly relate to an earlier date, in which case such representations and warranties are true and correct as of such earlier date); provided, that, for this purpose, the representations and warranties of the Company shall be deemed to be updated and modified by the information included in the Registration Statement, including but not limited to the final prospectus relating to the IPO, a copy of which Registration Statement which includes a statutory prospectus that meets the information requirements of Section 10 of the Securities Act shall have been furnished to the Investor prior to the Closing and on which the Investor shall be entitled to rely. “Registration Statement” means the registration statement on Form S-1, including any prospectus filed pursuant to Rule 424 under the Securities Act, and any free writing prospectuses, relating to the IPO.

2.1 Organization, Valid Existence and Qualification. The Company is a corporation duly organized and validly existing under the laws of the State of Delaware and has all requisite corporate power and authority to carry on its business as currently conducted. The Company is duly qualified to transact business as a foreign corporation in each jurisdiction in which it conducts its business, except where failure to be so qualified could not reasonably be expected to result, either individually or in the aggregate, in a material adverse effect on the Company’s financial condition, business or operations.

2.2 Registration Statement. The Registration Statement and any prospectus contained therein will not, as of the filing date of such Registration Statement, contain any untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary in order to make the statements therein, in light of the circumstances under which they were made, not misleading.

2.3 Authorization. All corporate action on the part of the Company, its officers, directors and shareholders necessary for the authorization, execution and delivery of this Agreement, the performance of all obligations of the Company hereunder, and the authorization, issuance, sale and delivery of the Shares, has been taken or will be taken prior to the Closing, and this Agreement constitutes the valid and legally binding obligation of the Company, enforceable in accordance with their respective terms, except (a) as limited by applicable bankruptcy, insolvency, reorganization, moratorium, and other laws of general application affecting enforcement of creditors’ rights generally, and (b) as limited by laws relating to the availability of specific performance, injunctive relief or other equitable remedies.

2.4 Valid Issuance of Shares. The Shares that are being purchased by the Investor hereunder, when issued, sold and delivered in accordance with the terms of this Agreement for the consideration expressed herein, will be duly and validly issued, fully paid, and nonassessable, and will be transferred to the Investor free of liens, encumbrances and restrictions on transfer other than (a) restrictions on transfer under applicable state and federal securities laws and (b) any liens, encumbrances or restrictions on transfer that are created or imposed by the Investor. Subject in part to the truth and accuracy of the

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Investor’s representations set forth in Section 3 of this Agreement, the offer, sale and issuance of the Shares as contemplated by this Agreement are exempt from the registration requirements of applicable state and federal securities laws.

2.5 Non-Contravention. No consent, approval, order or authorization of, or registration, qualification, designation, declaration or filing with, any federal, state or local governmental authority on the part of the Company is required in connection with the consummation of the sale and issuance of Shares contemplated by this Agreement, except for the filing of notices of the sale of Shares pursuant to Regulation D promulgated under the Securities Act and applicable state securities laws. The Company is not in violation or default in any material respect of any provision of its certificate of incorporation or bylaws, or of any instrument, judgment, order, writ or decree to which it is a party or by which it is bound, or, to its knowledge, of any provision of any federal or state statute, rule or regulation applicable to the Company, except for such violations or defaults of any federal or state statute, rule or regulation that could not reasonably be expected to result, either individually or in the aggregate, in a material adverse effect on the Company’s financial condition, business or operations. The execution, delivery and performance of this Agreement and the consummation of the transactions contemplated hereby will not result in any such violation or constitute, with or without the passage of time and giving of notice, either (i) a default in any material respect of any such instrument, judgment, order, writ or decree, or (ii) an event that results in the creation of any lien, charge or encumbrance upon any assets of the Company or the suspension, revocation, impairment, forfeiture, or nonrenewal of any material permit, license, authorization or approval applicable to the Company, in each case, which could reasonably be expected to result, either individually or in the aggregate, in a material adverse effect on the Company’s financial condition, business or operations.

3. Representations and Warranties of the Investor. The Investor hereby represents and warrants to the Company that the following representations are true and correct as of the date hereof and as of the Closing (except to the extent any such representations and warranties expressly relate to an earlier date, in which case such representations and warranties are true and correct as of such earlier date):

3.1 Authorization. The Investor has all requisite power and authority to enter into this Agreement and this Agreement constitutes its valid and legally binding obligations, enforceable in accordance with its terms except (a) as limited by applicable bankruptcy, insolvency, reorganization, moratorium, and other laws of general application affecting enforcement of creditors’ rights generally, and (b) as limited by laws relating to the availability of specific performance, injunctive relief, or other equitable remedies.

3.2 Purchase Entirely for Own Account. This Agreement is made with the Investor in reliance upon the Investor’s representations to the Company, which by the Investor’s execution of this Agreement the Investor hereby confirms, that the Shares acquired by the Investor hereunder will be acquired for investment for the Investor’s own account, not as a nominee or agent, and not with a view to the resale or distribution of any part thereof, and that the Investor has no present intention of selling, granting any participation in, or otherwise distributing the same. By executing this Agreement, the Investor further represents that the Investor does not have any contract, undertaking, agreement or arrangement with any person to sell, transfer or grant participation rights to such person or to any third person, with respect to any of the Shares.

3.3 No Solicitation. At no time was the Investor presented with or solicited by any publicly issued or circulated newspaper, mail, radio, television or other form of general advertising or solicitation in connection with the offer, sale and purchase of the Shares.

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3.4 Access to Information. The Investor has received or has had full access to all the information it considers necessary or appropriate to make an informed investment decision with respect to the Shares to be purchased by the Investor under this Agreement. The Investor further has had an opportunity to ask questions and receive answers from the Company regarding the terms and conditions of the offering of the Shares and to obtain additional information (to the extent the Company possessed such information or could acquire it without unreasonable effort or expense) necessary to verify any information furnished to the Investor or to which the Investor had access. The foregoing, however, does not in any way limit or modify the representations and warranties made by the Company in Section 2.

3.5 Investment Experience. The Investor understands that the purchase of the Shares involves substantial risk. The Investor has experience as an investor in securities of companies in the development stage and acknowledges that the Investor is able to fend for itself, can bear the economic risk of the Investor’s investment in the Shares, including a complete loss of the investment, and has such knowledge and experience in financial or business matters that the Investor is capable of evaluating the merits and risks of this investment in the Shares and protecting its own interests in connection with this investment. The Investor represents that the office in which its investment decision was made is located at the address set forth in Section 6.5.

3.6 Accredited Investor. The Investor understands the term “accredited investor” within the meaning of Rule 501 of Regulation D promulgated under the Securities Act and is an “accredited investor” for the purposes of acquiring the Shares to be purchased by the Investor under this Agreement.

3.7 Restricted Securities.

(a) The Investor understands that the Shares are characterized as “restricted securities” under the Securities Act inasmuch as they are being acquired from the Company in a transaction not involving a public offering and that under the Securities Act and applicable regulations thereunder such securities may be resold without registration under the Securities Act only in certain limited circumstances. The Investor represents that the Investor is familiar with Rule 144 of the Securities Act, as presently in effect, and understands the resale limitations imposed thereby and by the Securities Act.

(b) The Investor understands that the certificates evidencing the Shares may bear one or all of the following legends (or substantially similar legends):

THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), OR UNDER THE SECURITIES LAWS OF APPLICABLE STATES. THESE SECURITIES ARE SUBJECT TO RESTRICTIONS ON TRANSFERABILITY AND RESALE AND MAY NOT BE TRANSFERRED OR RESOLD EXCEPT AS PERMITTED UNDER THE ACT AND APPLICABLE STATE SECURITIES LAWS, PURSUANT TO REGISTRATION OR EXEMPTION THEREFROM. INVESTORS SHOULD BE AWARE THAT THEY MAY BE REQUIRED TO BEAR THE FINANCIAL RISKS OF THIS INVESTMENT FOR AN INDEFINITE PERIOD OF TIME.

3.8 No Brokers. The Investor has not incurred, and will not incur in connection with the purchase of the Shares, any brokerage or finders’ fees, or agents’ commissions or similar liabilities.

4. Conditions to the Investor’s Obligations at Closing. The obligations of the Investor at Closing are subject to the fulfillment or waiver, on or by Closing, of each of the following conditions, which waiver may be given by written, oral or telephone communication to the Company or its counsel.

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4.1 Representations and Warranties. Each of the representations and warranties of the Company contained in Section 2 shall be true and accurate in all material respects on and as of the Closing with the same force and effect as if they had been made at the Closing, except for (a) those representations and warranties that address matters only as of a particular date (which shall remain true and correct as of such particular date), with the same force and effect as if they had been made at the Closing, and (b) those representations and warranties which (i) are qualified as to materiality or (ii) provide that the Company’s failure to comply with such representation or warranty would not result in a material adverse effect, shall be true and accurate in every respect as of the Closing.

4.2 Performance. The Company shall have performed and complied in all material respects with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by it on or before the Closing and shall have obtained all approvals, consents and qualifications necessary to complete the purchase and sale described herein.

4.3 IPO. The Registration Statement shall have been declared effective by the SEC. The Underwriters shall have purchased the Firm Shares (as defined in the Underwriting Agreement) at the IPO Price (less any underwriting discounts or commissions).

4.4 Qualifications. All authorizations, approvals, or permits, if any, of any governmental authority or regulatory body of the United States or of any state that are required in connection with the lawful issuance and sale of the Shares pursuant to this Agreement shall be duly obtained and effective as of the Closing, other than (a) the filing pursuant to Regulation D, promulgated under the Securities Act, and (b) the filings required by applicable state “blue sky” securities laws, rules and regulations.

5. Conditions to the Company’s Obligations at Closing. The obligations of the Company to the Investor at the Closing are subject to the fulfillment, on or by the Closing, of each of the following conditions, which waiver may be given by written, oral or telephone communication to the Investor or its counsel:

5.1 Representations and Warranties. The representations and warranties of the Investor contained in Section 3 shall be true and accurate in all material respects on and as of the Closing with the same force and effect as if they had been made at the Closing.

5.2 Performance. The Investor shall have performed and complied in all material respects with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by it on or before the Closing and shall have obtained all approvals, consents and qualifications necessary to complete the purchase and sale described herein.

5.3 Payment of the Purchase Price. The Investor shall have delivered the Purchase Price as specified in Section 1.1 of this Agreement.

5.4 IPO. The Registration Statement shall have been declared effective by the SEC. The Underwriters shall have purchased the Firm Shares at the IPO Price (less any underwriting discounts or commissions).

5.5 IPO Lockup. The Investor shall have signed a customary lockup agreement requested by the Underwriters (the “Lockup Agreement”), including but not limited to an agreement not to sell, transfer, make any short sale of, grant any option for the purchase of, or enter into any hedging or similar transaction with the same economic effect as a sale, any Common Stock held by the Investor (other than those included in the registration) during the 180-day period following the effective date of the IPO.

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6. Miscellaneous.

6.1 Survival of Representations and Warranties. The representations and warranties of the Company and the Investor contained in or made pursuant to this Agreement shall survive the execution and delivery of this Agreement, and shall in no way be affected by any investigation of the subject matter thereof made by or on behalf of the Investor or the Company.

6.2 Governing Law. This Agreement shall be governed by and construed in accordance with the internal laws of the State of Delaware (without reference to the conflicts of law provisions thereof).

6.3 Counterparts; Facsimile Signatures. This Agreement may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument. This Agreement may be executed and delivered by facsimile, or by email in portable document format (.pdf) and upon such delivery of the signature page by such method will be deemed to have the same effect as if the original signature had been delivered to the other parties.

6.4 Headings; Interpretation. In this Agreement, (a) the meaning of defined terms shall be equally applicable to both the singular and plural forms of the terms defined, (b) the captions and headings are used only for convenience and are not to be considered in construing or interpreting this Agreement and (c) the words “including,” “includes” and “include” shall be deemed to be followed by the words “without limitation.” All references in this Agreement to sections, paragraphs, exhibits and schedules shall, unless otherwise provided, refer to sections and paragraphs hereof and exhibits and schedules attached hereto, all of which exhibits and schedules are incorporated herein by this reference.

6.5 Notices. All notices which are required or permitted hereunder shall be in writing and sufficient if delivered personally, sent by facsimile or email (and promptly confirmed by personal delivery, registered or certified mail or overnight courier), sent by nationally-recognized overnight courier or sent by registered or certified mail, postage prepaid, return receipt requested, addressed as follows:

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6.6 No Finder’s Fees. The Investor agrees to indemnify and to hold harmless the Company from any liability for any commission or compensation in the nature of a finders’ or broker’s fee (and any asserted liability as a result of the performance of services of any such finder or broker) for which the Investor or any of its officers, partners, employees, or representatives is responsible. The Company agrees to indemnify and hold harmless the Investor from any liability for any commission or compensation in the nature of a finder’s or broker’s fee (and any asserted liability as a result of the performance of services by any such finder or broker) for which the Company or any of its officers, employees or representatives is responsible.

6.7 Amendments and Waivers. Any term of this Agreement may be amended and the observance of any term of this Agreement may be waived (either generally or in a particular instance and either retroactively or prospectively), only with the written consent of the Company and the Investor. No delay or failure to require performance of any provision of this Agreement shall constitute a waiver of that provision as to that or any other instance. No waiver granted under this Agreement as to any one provision herein shall constitute a subsequent waiver of such provision or of any other provision herein, nor shall it constitute the waiver of any performance other than the actual performance specifically waived.

6.8 Severability. If any provision of this Agreement is determined by any court or arbitrator of competent jurisdiction to be invalid, illegal or unenforceable in any respect, such provision will be enforced to the maximum extent possible given the intent of the parties hereto. If such clause or provision cannot be so enforced, such provision shall be stricken from this Agreement and the remainder of this Agreement shall be enforced as if such invalid, illegal or unenforceable clause or provision had (to the extent not enforceable) never been contained in this Agreement.

6.9 Entire Agreement. This Agreement, together with all exhibits and schedules hereto, constitute the entire agreement and understanding of the parties with respect to the subject matter hereof and supersede any and all prior negotiations, correspondence, agreements, understandings duties, or obligations, whether oral or written, between or among the parties hereto with respect to the specific subject matter hereof.

6.10 Third Parties. Nothing in this Agreement, express or implied, is intended to confer upon any person, other than the parties hereto and their successors and assigns, any rights or remedies under or by reason of this Agreement.

6.11 Costs, Expenses. The Company and the Investor will each bear their own expenses in connection with the preparation, execution and delivery of this Agreement and the consummation of the Financing.

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6.12 Further Assurances. The parties agree to execute such further documents and instruments and to take such further actions as may be reasonably necessary to carry out the purposes and intent of this Agreement.

6.13 Termination. This Agreement shall automatically terminate upon the earliest to occur, if any, of: (a) either the Company, on the one hand, or the Underwriters, on the other hand, advising the other in writing, prior to the execution of the Underwriting Agreement, that they have determined not to proceed with the IPO, (b) termination of the Underwriting Agreement (other than the provisions thereof which survive termination) prior to the sale of any of the Common Stock to the Underwriters in the IPO, (c) the registration statement filed with the SEC with respect to the IPO is withdrawn, (d) the Underwriting Agreement has not become effective by December 31, 2018 (or, if the Company exercises its option to extend the term of the Lockup Agreement to March 31, 2019 pursuant to the terms of such agreement, if the Underwriting Agreement has not become effective by March 31, 2019), (e) the termination of that certain Exclusive Patent License and Research Collaboration Agreement, dated as of July 23^rd, 2018, by and between the Company and the Investor or (f) the written consent of each of the Company and the Investor.

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IN WITNESS WHEREOF, the parties hereto have executed this COMMON STOCK PURCHASE AGREEMENT as of the date first written above.

[Signature Page to Common Stock Purchase Agreement]

IN WITNESS WHEREOF, the parties hereto have executed this COMMON STOCK PURCHASE AGREEMENT as of the date first written above.

[Signature Page to Common Stock Purchase Agreement]