Exhibit 5.1

787 Seventh Avenue New York, NY 10019-6099 Tel: 212 728 8000 Fax: 212 728 8111

September 28, 2026

Kyndryl Holdings, Inc.

One Vanderbilt Avenue, 15th Floor

New York, New York 10017

Re: Offering of Senior Notes

Ladies and Gentlemen:

We have acted as special counsel to Kyndryl Holdings, Inc., a Delaware corporation (the “Company”), in connection with the sale by the Company of $600,000,000 aggregate principal amount of its 7.800% Senior Notes due 2029 (the “2029 Notes”) and $400,000,000 aggregate principal amount of its 7.875% Senior Notes due 2032 (the “2032 Notes” and, together with the 2029 Notes, the “Notes”), pursuant to that certain Underwriting Agreement, dated September 24, 2026 (the “Underwriting Agreement”), by and among the Company and J.P. Morgan Securities LLC, Citigroup Global Markets Inc. and Morgan Stanley & Co. LLC, as representatives of the underwriters named therein (the “Underwriters”). The Notes were issued pursuant to an indenture, dated as of October 15, 2021 (the “Base Indenture”), between the Company and The Bank of New York Mellon Trust Company, N.A., as trustee (the “Trustee”), as supplemented by a Third Supplemental Indenture relating to the 2029 Notes (the “Third Supplemental Indenture”) and a Fourth Supplemental Indenture relating to the 2032 Notes (the “Fourth Supplemental Indenture” and, together with the Third Supplemental Indenture, the “Supplemental Indentures”), each dated as of September 28, 2026, between the Company and the Trustee. The Base Indenture as supplemented by the Supplemental Indentures is herein referred to as the “Indenture.” The Notes are being offered pursuant to Rule 415 under the Securities Act of 1933, as amended (the “Securities Act”). This opinion is being delivered in connection with that certain Registration Statement on Form S-3 (No. 333-276713), originally filed with the Securities and Exchange Commission (the “Commission”) on January 26, 2024 (the “Registration Statement”) and the related prospectus contained in the Registration Statement, as supplemented by the final prospectus supplement relating to the Notes, dated September 24, 2026, filed with the Commission pursuant to Rule 424 under the Securities Act (as so supplemented, the “Prospectus”).

We have examined such documents as we have considered necessary for purposes of this opinion, including (i) the Registration Statement, (ii) the Prospectus, (iii) the Indenture, (iv) copies of the certificate of incorporation and by-laws of the Company, (v) the Underwriting Agreement, (vi) the form of global certificate evidencing the 2029 Notes, (vii) the form of global certificate evidencing the 2032 Notes, (viii) a certificate of the Secretary of the Company, dated September 28, 2026, including the exhibits thereto, (ix) a certificate, dated September 16, 2026, and a facsimile bringdown thereof, dated September 28, 2026, from the Office of the Secretary of the State of Delaware as to the existence and good standing in the State of Delaware of the Company and (x) such other documents and matters of law as we have deemed necessary in connection with the opinions hereinafter expressed.

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Kyndryl Holdings, Inc.
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As to questions of fact material to the opinions expressed below, we have relied without independent check or verification upon certificates and comparable documents of public officials and officers and representatives of the Company and statements of fact contained in the documents we have examined. In our examination and in rendering our opinions contained herein, we have assumed (i) the genuineness of all signatures of all parties; (ii) the authenticity of all corporate records, documents, agreements, instruments and certificates submitted to us as originals and the conformity to original documents and agreements of all documents and agreements submitted to us as conformed, certified or photostatic copies; (iii) the due organization, valid existence and good standing of all parties (other than the Company) under all applicable laws; (iv) the legal right and power of all parties (other than the Company) under all applicable laws and regulations to enter into, execute and deliver such documents, agreements and instruments; (v) the due authorization, execution and delivery of the Registration Statement and due authorization of all documents, agreements and instruments (including the Indenture) by all parties thereto (other than the Company) and the binding effect of such documents, agreements and instruments on all parties (other than the Company); (vi) that all consents, approvals and authorizations by any governmental authority required to be obtained by all parties (other than the Company) have been obtained by such parties; and (vii) the capacity of natural persons. In addition, we have reviewed the originals or copies certified or otherwise identified to our satisfaction of all such corporate records of the Company and such other instruments and other certificates of public officials, officers and representatives of the Company and such other persons, and we have made such investigations of law, as we have deemed appropriate as a basis for the opinion expressed below.

Based on the foregoing, and subject to the further assumptions and qualifications set forth below, it is our opinion that the Notes have been duly authorized and, when they have been duly executed and authenticated in accordance with the provisions of the Indenture and delivered to and paid for by the Underwriters in accordance with the terms of the Underwriting Agreement, will be valid, binding and enforceable obligations of the Company, entitled to the benefits of the Indenture.

The opinions expressed herein are limited to the laws of the State of New York, the General Corporation Law of the State of Delaware and the federal laws of the United States as in effect on the date of this letter and typically applicable to transactions of the type contemplated in this letter and to the specific legal matters expressly addressed herein, and no opinion is expressed or implied with respect to the laws of any other jurisdiction or any legal matter not expressly addressed herein.

The opinions set forth above are qualified in that the legality or enforceability of the documents referred to therein may be (a) subject to applicable bankruptcy, insolvency, reorganization, moratorium or similar laws affecting creditors' rights generally, (b) limited insofar as the remedies of specific performance and injunctive and other forms of equitable relief may be subject to equitable defenses and the discretion of the court before which any enforcement thereof may be sought, and (c) subject to general principles of equity (regardless of whether enforceability is considered in a proceeding at law or in equity) including principles of commercial reasonableness or conscionability and an implied covenant of good faith and fair dealing. Insofar as provisions of any of the documents referenced in this letter provide for indemnification or contribution, the enforcement thereof may be limited by public policy considerations.

Kyndryl Holdings, Inc.
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We hereby consent to the use of our name in the Prospectus, under the heading “Legal Matters,” as counsel for the Company who has passed on the validity of the Notes and to the filing of this opinion as Exhibit 5.1 to the Company’s Current Report on Form 8-K dated September 28, 2026. In giving such consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act.

The opinion expressed herein is rendered on and as of the date hereof, and we assume no obligation to advise you, or to make any investigations, as to any legal developments or factual matters arising subsequent to the date hereof that might affect the opinion expressed herein.