Exhibit 5.1

Proskauer Rose LLP   Eleven Times Square   New York, NY 10036-8299

February 20, 2018

Celgene Corporation

86 Morris Avenue

Summit, NJ 07901

Ladies and Gentlemen:

We have acted as special counsel for Celgene Corporation, a Delaware corporation (the “Company”), with respect to the preparation of the Registration Statement on Form S-3 (the “Registration Statement”) filed on October 27, 2016 with the Securities and Exchange Commission (the “Commission”) in connection with the registration by the Company under the Securities Act of 1933, as amended (the “Securities Act”), of the offer and sale by the Company from time to time, pursuant to Rule 415 under the Securities Act, of senior debt securities of the Company. $500,000,000 aggregate principal amount of 2.875% Senior Notes due 2021 (the “2021 Notes”), $1,000,000,000 aggregate principal amount of 3.250% Senior Notes due 2023 (the “2023 Notes”), $1,500,000,000 aggregate principal amount of 3.900% Senior Notes due 2028 (the “2028 Notes”) and $1,500,000,000 aggregate principal amount of 4.550% Senior Notes due 2048 (the “2048 Notes” and, together with the 2021 Notes, the 2023 Notes and the 2028 Notes, the “Notes”) are being issued by the Company and are being offered and sold by the Company pursuant to the base prospectus forming a part of the Registration Statement, as supplemented by the Prospectus Supplement, dated February 8, 2018 (together, the “Prospectus”), filed by the Company with the Commission pursuant to Rule 424(b) under the Securities Act, and an Underwriting Agreement, dated February 8, 2018 (the “Underwriting Agreement”), among the Company and the Managers named in Schedule I thereto for the Underwriters named in Schedule II thereto. The Notes will be issued under an Indenture, dated as of February 20, 2018 (the “Indenture”), between the Company and The Bank of New York Mellon Trust Company, N.A., as trustee (the “Trustee”).

We have examined: (i) the Registration Statement; (ii) the Prospectus; (iii) the bylaws of the Company as amended and currently in effect; (iv) the Certificate of Incorporation of the Company, as amended and restated and further amended to date; (v) the Indenture; and (vi) such other documents as we have deemed necessary or appropriate for purposes of this opinion.

Based upon and subject to the foregoing, we are of the opinion that, when the Notes have been duly executed, authenticated, issued and delivered in accordance with the terms of the Indenture and the Underwriting Agreement, and upon payment of the consideration therefor or provided for therein, the Notes will constitute legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, except as such enforcement may be subject to any applicable bankruptcy, insolvency, reorganization, fraudulent conveyance or other law relating to or affecting creditors’ rights generally and general principles of equity.

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February 20, 2018

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The opinion expressed herein is qualified in the following respects:

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Company’s Current Report on Form 8-K filed on or about the date hereof and to the references to this firm under the caption “Legal Matters” in the Prospectus included in the Registration Statement. In giving such 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.