Exhibit 5.1

March 2, 2011

State Street Corporation

One Lincoln Street

Boston, Massachusetts 02111

2.875% Senior Notes due 2016

4.375% Senior Notes due 2021

Ladies and Gentlemen:

We have acted as counsel for State Street Corporation, a Massachusetts corporation (the “Company”), in connection with the offer and sale of $250,000,000 aggregate principal amount of the Company’s Floating Rate Senior Notes due 2014 (the “2014 Notes”), $1,000,000,000 aggregate principal amount of the Company’s 2.875% Senior Notes due 2016 (the “2016 Notes”) and $750,000,000 aggregate principal amount of the Company’s 4.375% Senior Notes due 2021 (the “2021 Notes,” and together with the 2014 Notes and the 2016 Notes, the “Debt Securities”), pursuant to an Underwriting Agreement, dated as of March 2, 2011 (the “Underwriting Agreement”), among the Company and Morgan Stanley & Co. Incorporated and Merrill Lynch, Pierce, Fenner & Smith Incorporated, as representatives of the several underwriters named in the Underwriting Agreement. The Debt Securities will be issued pursuant to an Indenture, dated as of March 11, 2009 (the “Indenture”), between the Company and U.S. Bank National Association (the “Trustee”).

As such counsel, we have assisted in the preparation and filing with the Securities and Exchange Commission (the “Commission”) of the Company’s prospectus supplement dated March 2, 2011 (the “Prospectus Supplement”) to the prospectus, dated March 12, 2009 (the “Base Prospectus”), each relating to the registration statement on Form S-3 (File No. 333-157882) (the “Registration Statement”) filed by the Company with the Commission on March 12, 2009.

We have examined and relied upon corporate or other proceedings of the Company regarding (i) the authorization of the execution and delivery of the Indenture, the Underwriting Agreement and the issuance of the Debt Securities, (ii) the Registration Statement, (iii) the Base Prospectus, (iv) the Prospectus Supplement, (v) the Underwriting Agreement and (vi) the Indenture. We have also examined and relied upon originals or copies, certified or otherwise identified to our satisfaction, of such other corporate records of the Company, such other agreements and instruments, certificates of public officials and such other documents,

Wilmer Cutler Pickering Hale and Dorr LLP, 399 Park Avenue, New York, New York 10022

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March 2, 2011

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instruments and certificates as we have deemed necessary as a basis for the opinions hereinafter expressed.

In our examination of the documents referred to above, we have assumed the genuineness of all signatures, the legal capacity of all individual signatories, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as copies, the authenticity of such original documents, and the completeness and accuracy of the corporate records of the Company provided to us by the Company.

In rendering the opinions set forth below, we have assumed that (i) the Trustee has the power, corporate or other, to enter into and perform its obligations under the Indenture, (ii) the Indenture will be a valid and binding obligation of the Trustee, and (iii) the Trustee shall have been qualified under the Trust Indenture Act of 1939, as amended. We have also assumed the due authentication of the Debt Securities by the Trustee, that there will not have occurred, prior to the date of issuance of the Debt Securities, any change in law affecting the validity or enforceability of such Debt Securities and that at the time of the issuance and sale of the Debt Securities, the Board of Directors of the Company has not taken any action to rescind or otherwise reduce its prior authorization of the issuance of the Debt Securities.

We express no opinion herein as to the laws of any jurisdiction other than the state laws of the State of New York and the federal laws of the United States of America.

We have assumed for purposes of our opinions below that no authorization, approval or other action by, and no notice to or filing with, any governmental authority or regulatory body or (to the extent the same is required under any agreement or document binding on it of which an addressee has knowledge, has received notice or has reason to know) any other third party is required for the due execution, delivery or performance by the Company of the Indenture or the Debt Securities or, if any such authorization, approval, consent, action, notice or filing is required, it will have been duly obtained, taken, given or made and will be in full force and effect.

Our opinions below are qualified to the extent that they may be subject to or affected by (i) applicable bankruptcy, insolvency, reorganization, moratorium, usury, fraudulent conveyance or similar laws relating to or affecting the rights or remedies of creditors generally, (ii) duties and standards imposed on creditors and parties to contracts, including, without limitation, requirements of materiality, good faith, reasonableness and fair dealing, and (iii) general equitable principles. Furthermore, we express no opinion as to the availability of any equitable or specific remedy upon any breach of the Indenture or the Debt Securities, or to the successful assertion of any equitable defenses, inasmuch as the availability of such remedies or the success of any equitable defenses may be subject to the discretion of a court. We also express no opinion herein with respect to compliance by the Company with the securities or “blue sky” laws of any state or other jurisdiction of the United States or of any foreign jurisdiction. In addition, we

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March 2, 2011

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express no opinion and make no statement herein with respect to the antifraud laws of any jurisdiction.

On the basis of, and subject to, the foregoing, we are of the opinion that when the Debt Securities have been duly executed by the Company and duly authenticated by the Trustee in accordance with the terms of the Indenture, and delivered to the purchasers thereof against payment of the consideration therefor duly approved by the Company, and subject to the final terms of the Debt Securities not resulting in a default under or a breach of any agreement or instrument binding upon the Company and complying with any requirement or restriction imposed by any court or governmental entity having jurisdiction over the Company, the Debt Securities will constitute valid and binding obligations of the Company, enforceable against the Company, in accordance with their terms.

Please note that we are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matters. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions and is rendered as of the date hereof, and we disclaim any obligation to advise you of any change in any of the foregoing sources of law or subsequent developments in law or changes in facts or circumstances that might affect any matters or opinions set forth herein.

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Company’s Current Report on Form 8-K to be filed on or about March 7, 2011, which Form 8-K will be incorporated by reference into the Registration Statement and to the use of our name therein and in the related Base Prospectus and Prospectus Supplement under the caption “Legal Matters.” 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 of 1933, as amended, or the rules and regulations of the Commission.

Very truly yours,