Exhibit 5.1

Ladies and Gentlemen:

We have acted as special counsel to Citigroup Inc. (the “Company”), a Delaware corporation, in connection with the public offering of 23,000,000 depositary shares (the “Depositary Shares”), representing an aggregate of 23,000 shares (the “Preferred Shares”) of the Company’s 5.80% Noncumulative Preferred Stock, Series C, par value $1.00 and $25,000 liquidation preference per share (the “Preferred Stock”). The Preferred Shares are to be deposited with Computershare Inc. and Computershare Trust Company, N.A. (“Computershare Trust”) acting jointly as depositary (collectively, the “Depositary”), pursuant to the Deposit Agreement, dated March 26, 2013 (the “Deposit Agreement”), among the Company, the Depositary, as depositary, Computershare Trust, as registrar and transfer agent, and the holders from time to time of receipts issued under the Deposit Agreement to evidence the Depositary Shares. On March 19, 2013, the Company entered into an Underwriting Agreement, dated March 19, 2013 (the “Underwriting Agreement”), with Citigroup Global Markets Inc., as representative of the underwriters named therein (the “Underwriters”), relating to the sale by the Company to the Underwriters of the Depositary Shares.

This opinion is being delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act (as defined below).

In connection with this opinion, we have examined originals or copies, certified or otherwise identified to our satisfaction, of (i) the registration statement on Form S-3 (File No. 333-172562) of the Company, relating to preferred stock, depositary shares and other securities of the Company, filed with the Securities and Exchange Commission (the “Commission”) on May 11, 2011 under the Securities Act of 1933, as amended (the “Securities Act”), allowing for delayed offerings pursuant to Rule 415 of the General Rules and Regulations under the Securities Act (the “Rules and Regulations”) (such registration statement being hereinafter referred to as the “Registration Statement”), (ii) an executed copy of the Underwriting Agreement, (iii) an executed copy of the Deposit Agreement; (iv) an executed certificate evidencing the Preferred Shares registered in the name of Computershare Trust Company, N.A., (v) an executed Receipt registered in the name of Cede & Co., relating to

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23,000,000 Depositary Shares (the “Receipts”); (vi) the Certificate of Designations (the “Certificate of Designations”) designating the Preferred Stock, as filed with the Secretary of State of the State of Delaware on March 25, 2013 and certified by such Secretary of State; (vii) a copy of the Company’s Restated Certificate of Incorporation, as amended and in effect as of the date hereof, as certified by Michael J. Tarpley, Assistant Secretary of the Company (the “Assistant Secretary”); (viii) the By-Laws of the Company, as amended and as in effect on the date hereof, as certified by the Assistant Secretary; and (ix) a copy of certain resolutions of the Board of Directors of the Company, adopted on October 17, 2012 and certain resolutions of the Pricing Committee thereof, adopted on March 19, 2013, as certified by the Assistant Secretary. We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such other documents, certificates and records as we have deemed necessary or appropriate as a basis for the opinions set forth herein.

In our examination, we have assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified or photostatic copies and the authenticity of the originals of such copies. In making our examination of executed documents, we have assumed that the parties thereto, other than the Company, had the power, corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and execution and delivery by such parties of such documents and that such documents constitute valid and binding obligations of such parties. As to any facts material to the opinions expressed herein that were not independently established or verified, we have relied upon oral or written statements and representations of officers, trustees and other representatives of the Company and others.

We do not express any opinion as to any laws other than Delaware corporate law and statutory trust law and the laws of the State of New York. Insofar as the opinions expressed herein relate to matters governed by laws other than those set forth in the preceding sentence, we have assumed, without having made any independent investigation, that such laws do not affect any of the opinions set forth herein. The opinions expressed herein are based on laws in effect on the date hereof, which laws are subject to change with possible retroactive effect.

Based on and subject to the foregoing and to the other qualifications and limitations set forth herein, we are of the opinion that:

1. The Preferred Shares have been duly authorized by all requisite corporate action on the part of the Company under the Delaware General Corporation Law (the “DGCL”) and, when the Preferred Stock Certificate is delivered to and paid for in accordance with the terms of the Underwriting Agreement, will be validly issued, fully paid and nonassessable.

2. The Receipts, when issued under the Deposit Agreement in accordance with the provisions of the Deposit Agreement and upon payment by the Underwriters in accordance with the Underwriting Agreement, will be legally issued and will entitle the holders thereof to the rights specified in such Receipts and in the Deposit Agreement.

The opinions stated herein are subject to the following qualifications:

(a) the opinions stated herein are limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent transfer, preference and other similar laws affecting creditors’ rights generally, and by general principles of equity (regardless of whether enforcement is sought in equity or at law);

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(b) except to the extent expressly stated in the opinions contained herein, we do not express any opinion with respect to the effect on the opinions stated herein of (i) the compliance or non-compliance of any party to the Underwriting Agreement or the Deposit Agreement with any laws, rules or regulations applicable to such party or (ii) the legal status or legal capacity of any such party to the Underwriting Agreement or the Deposit Agreement;

(c) we do not express any opinion with respect to any law, rule or regulation that is applicable to any party to the Underwriting Agreement or the Deposit Agreement or the transactions contemplated thereby solely because such law, rule or regulation is part of a regulatory regime applicable to any such party or any of its affiliates as a result of the specific assets or business operations of such party or such affiliates; and

(d) we have assumed that the certificate evidencing the Preferred Shares was manually signed by one of the authorized officers of the transfer agent and registrar for the Preferred Stock and registered by such transfer agent and registrar.

In addition, in rendering the foregoing opinions we have assumed that neither the execution and delivery by the Company of the Underwriting Agreement or the Deposit Agreement nor the consummation by the Company of the transactions contemplated thereby, including the issuance and sale of the Depositary Shares representing the Preferred Shares: (i) constitutes or will constitute a violation of, or a default under, any lease, indenture, instrument or other agreement to which the Company or its property is subject, (ii) contravenes or will contravene any order or decree of any governmental authority to which the Company or its property is subject, or (iii) violates or will violate any law, rule or regulation to which the Company or its property is subject.

We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Company’s Current Report on Form 8-K being filed on the date hereof, and incorporated by reference into the Registration Statement. We also hereby consent to the reference to our firm under the caption “Legal Matters” in the prospectus supplement dated March 19, 2013 and filed with the Commission. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission promulgated thereunder. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable law.

Very truly yours,

/s/ Skadden, Arps, Slate, Meagher & Flom LLP