Exhibit 5.1

May 5, 2015

Bristol-Myers Squibb Company

345 Park Avenue

New York, NY 10154

Ladies and Gentlemen:

We have acted as counsel to Bristol-Myers Squibb Company, a Delaware corporation (the “Company”), in connection with the registration by the Company under the Securities Act of 1933 (the “Securities Act”) of €575,000,000 in aggregate principal amount of the Company’s 1.000% Notes due 2025 (the “2025 Notes”) and €575,000,000 in aggregate principal amount of the Company’s 1.750% Notes due 2035 (the “2035 Notes” and, together with the 2025 Notes, the “Notes”) issued pursuant to the Indenture, dated as of June 1, 1993 (as heretofore supplemented, the “Indenture”), between the Company and The Bank of New York Mellon (as successor to The Chase Manhattan Bank (National Association)), as trustee (the “Trustee”), pursuant to the registration statement on Form S-3 (File No. 333-182852), filed with the Securities and Exchange Commission (the “Commission”) on July 26, 2012 (such registration statement, as amended to the date hereof, is herein referred to as the “Registration Statement”).

Bristol-Myers Squibb Company

May 5, 2015

Page 2

We have reviewed such corporate records, certificates and other documents, and such questions of law, as we have considered necessary or appropriate for the purposes of this opinion. We have assumed that all signatures are genuine, that all documents submitted to us as originals are authentic and that all copies of documents submitted to us conform to the originals. We have assumed further that the Trustee and its predecessor trustee have duly authorized, executed and delivered the Indenture.

Additionally, we have relied as to certain matters on information obtained from public officials, officers of the Company and other sources believed by us to be responsible.

Based on the foregoing and subject to the qualifications set forth herein, we are of the opinion that, when the Notes have been (a) duly executed by the Company and duly authenticated and delivered by the Trustee in accordance with the Indenture and (b) duly issued and delivered by the Company against payment of the purchase price therefor as contemplated in the Registration Statement, the Notes will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equity principles.

We are members of the bar of the State of New York. We do not express any opinion herein on any laws other than the law of the State of New York.

Bristol-Myers Squibb Company

May 5, 2015

Page 3

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Current Report on Form 8-K that will be incorporated by reference into the Registration Statement. We also hereby consent to the reference to our firm under the heading “Validity of the Securities” in the prospectus constituting part of the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Covington & Burling LLP