EXHIBIT 5.1

599 Lexington Avenue

New York, NY 10022-6069

+1.212.848.4000

May 20, 2020

Boston Scientific Corporation

300 Boston Scientific Way

Marlborough, Massachusetts 01752-1234

Ladies and Gentlemen:

We have acted as counsel to Boston Scientific Corporation, a Delaware corporation (the “Company”), in connection with the preparation and filing by the Company of a registration statement on Form S-3ASR (such registration statement, including the documents incorporated by reference therein, the “Registration Statement”) with the Securities and Exchange Commission (the “Commission”) relating to the registration of an indeterminate aggregate amount of (i) shares of the Company’s common stock, par value $0.01 per share (“Common Stock”), (ii) shares of the Company’s preferred stock, par value $0.01 per share (“Preferred Stock”), including such shares of Common Stock as may be issued upon conversion of the Company’s Preferred Stock or as stock dividends in respect of the Company’s Preferred Stock and such shares of Common Stock as may be issued pursuant to anti-dilution adjustments determined at the time of offering (collectively, “Indeterminate Securities” and together with the Common Stock and the Preferred Stock, the “Securities.”). Any offering of Securities will be made by the Company from time to time, pursuant to Rule 415 of the Securities Act of 1933, as amended (the “Securities Act”), as set forth in the prospectus contained in the Registration Statement (the “Prospectus”), as supplemented by one or more supplements to the Prospectus (each, a “Prospectus Supplement”) and as shall be designated by the Company at the time of the applicable offering pursuant to an applicable underwriting agreement in connection with the issuance and sale of the Securities (“Underwriting Agreement”).

The Preferred Stock will be issued in one or more series and the relative powers, designations, preferences, rights and qualifications, limitations or restrictions of such Preferred Stock will be set forth in one or more certificates of designation (each, a “Certificate of Designation”). Each Certificate of Designation will be in a form to be filed as an exhibit to a Current Report on Form 8-K incorporated in the Registration Statement by reference.

In that connection, we have reviewed originals or copies of the following documents:

(a) The Registration Statement;

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(b) The Third Restated Certificate of Incorporation and Amended and Restated By-laws of the Company; and

(c) Originals or copies of such other records of the Company, certificates of public officials and officers of the Company and agreements and other documents as we have deemed necessary as a basis for the opinions expressed below.

In our review, we have assumed:

(a) The genuineness of all signatures.

(b) The authenticity of the originals of the documents submitted to us.

(d) As to matters of fact, the truthfulness of the representations made in certificates of public officials and officers of the Company.

In our opinions stated below, we assume that all of the following (collectively, the “general conditions”) shall have occurred prior to the issuance of the Securities referred to therein:

(a) the Registration Statement, as finally amended (including all necessary post-effective amendments), has become effective under the Securities Act, and no stop order suspending its effectiveness will have been issued and remain in effect;

(b) an appropriate prospectus supplement or term sheet with respect to such Securities has been prepared, delivered and filed in compliance with the Securities Act;

(c) the applicable Underwriting Agreements shall have been duly authorized, executed and delivered by the Company and the other parties thereto;

(d) the terms of the applicable Underwriting Agreements and the issuance and sale of such Securities do not and will not:

i. contravene the Third Restated Certificate of Incorporation or Amended and Restated By-laws of the Company;

ii. violate any law, rule or regulation applicable to the Company; or

iii. result in any conflict with or breach of any agreement or document binding on the Company; and

(e) the number of shares of Common Stock or Preferred Stock issued pursuant to the Registration Statement, together with the number of shares of Common Stock or Preferred Stock, as applicable, outstanding or reserved at the time of issuance, will not exceed the respective number of shares authorized by the Company’s Third Restated Certificate of Incorporation in effect at the time of such issuance;

(f) no authorization, approval, consent or other action by, and no notice to or filing with, any governmental authority or regulatory body or any other third party is required for the due execution, delivery or performance by the Company of any of the Underwriting Agreements to which the Company is a party or, if any such authorization, approval, consent, action, notice or filing is required, it has been duly obtained, taken, given or made and is in full force and effect.

We have not independently established the validity of the foregoing assumptions.

“Generally Applicable Law” means the federal law of the United States of America, and the law of the State of New York (including, in each case, the rules or regulations promulgated thereunder or pursuant thereto), that a New York lawyer exercising customary professional diligence would reasonably be expected to recognize as being applicable to the Company, the Underwriting Agreements and for purposes of our opinions below, the General Corporation Law of the State of Delaware. Without limiting the generality of the foregoing definition of Generally Applicable Law, the term “Generally Applicable Law” does not include any law, rule or regulation that is applicable to the Company, the Underwriting Agreements or such transactions solely because such law, rule or regulation is part of a regulatory regime applicable to any party to any of the Underwriting Agreements or any of its affiliates due to the specific assets or business of such party or such affiliate.

Based upon the foregoing and upon such other investigation as we have deemed necessary and subject to the assumptions and qualifications set forth herein, we are of the opinion that:

1. When the general conditions have been satisfied and (i) the final terms of issuance and sale of the applicable shares of Common Stock, including any Indeterminate Securities constituting Common Stock, have been duly established and approved by the board of directors of the Company in conformity with the Company’s Third Restated Certificate of Incorporation, (ii) all corporate action necessary for issuance of the Common Stock has been taken, and (iii) such shares of Common Stock are issued and delivered to the purchasers thereof against payment of the consideration therefor (in an amount in excess of the par value thereof in the case of newly issued shares) duly approved by the board of directors of the Company, such shares of Common Stock will be duly authorized, validly issued, fully paid and non-assessable.

2. When the general conditions have been satisfied and (i) the final terms of Preferred Stock have been duly established and approved by the board of directors of the Company in conformity with the Company’s Third Restated Certificate of Incorporation, (ii) all corporate action necessary for issuance of the Preferred Stock has been taken, including the adoption and filing of a certificate of designation relating thereto with the Secretary of State of the State of Delaware, and (iii) such shares of Preferred Stock are issued and delivered to the purchasers thereof against payment of the consideration therefor (in an amount in excess of the par value thereof in the case of newly issued shares) duly approved by the board of directors of the Company, the Preferred Stock will be duly authorized, validly issued, fully paid and non-assessable.

Our opinions expressed above are subject to the following qualifications:

(a) Our opinion in paragraph 2 is subject to the effect of any applicable bankruptcy, insolvency, reorganization, moratorium or similar laws affecting creditors’ rights generally (including without limitation all laws relating to fraudulent transfers).

(b) Our opinion in paragraph 2 is also subject to the effect of general principles of equity, including without limitation concepts of materiality, reasonableness, good faith and fair dealing (regardless of whether considered in a proceeding in equity or at law).

(c) Our opinions are limited to Generally Applicable Law and we do not express any opinion herein concerning any other law.

This opinion letter is rendered to you in connection with the preparation and filing of the Registration Statement. This opinion letter may not be relied upon by you for any other purpose without our prior written consent.

This opinion letter speaks only as of the date hereof. We expressly disclaim any responsibility to advise you of any development or circumstance of any kind, including any change of law or fact, that may occur after the date of this opinion letter and which might affect the opinions expressed herein.

We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement and to the use of our name under the heading “Legal Matters” in the Prospectus. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Shearman & Sterling LLP

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