Exhibit 5.1

[Sullivan & Cromwell LLP Letterhead]

August 24, 2018

Royal Bank of Canada,

200 Bay Street,

Royal Bank Plaza,

Toronto, Ontario,

Canada M5J 2J5.

Ladies and Gentlemen:

In connection with the registration under the Securities Act of 1933 (the “Act”), of U.S. $40,000,000,000 aggregate initial offering price of (i) debt securities which may be senior obligations (the “Senior Debt Securities”) or subordinated obligations (the “Subordinated Debt Securities” and, together with the Senior Debt Securities, the “Debt Securities”) and (ii) warrants (the “Warrants” and, together with the Debt Securities, the “Securities”) of Royal Bank of Canada, a bank organized under the laws of Canada (the “Bank”), we, as your United States counsel, have examined 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.

Upon the basis of such examination, we advise you that, in our opinion, when the registration statement relating to the Securities (the “Registration Statement”) has become effective under the Act, each of the Third Supplemental Indenture relating to the Senior Debt Securities (the “Senior Debt Supplemental Indenture”), supplementing the Indenture, dated as of October 23, 2003, between the Bank and The Bank of New York Mellon, as successor to JPMorgan Chase Bank, N.A., as Trustee (as supplemented, the “Indenture”), and the indenture relating the Warrants (the “Warrant Indenture”) has been duly authorized, executed and delivered, the terms of the Securities and of their issuance and sale have been duly established in conformity with the respective indenture relating to each series of Securities (the “Applicable Indenture”) so as not to violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Bank and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Bank, and the Securities have been duly executed and authenticated in accordance with the Applicable Indenture and issued and sold as contemplated in the Registration Statement, the Securities will constitute valid and legally binding obligations of the Bank, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equity principles;

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provided, however, that we express no opinion with respect to the subordination provisions of the Subordinated Debt Securities and the provisions relating to an NVCC Automatic Conversion upon the occurrence of a Non-Viability Trigger Event (as such terms are defined in the First Supplemental Indenture relating to the Subordinated Debt Securities, supplementing the Indenture, dated as of January 27, 2016, among the Bank, The Bank of New York Mellon, as Trustee and BNY Trust Company of Canada, as Canadian Trustee), and the provisions of the Indenture relating to seniority of the Senior Debt Securities and the acknowledgement of Holders and Beneficial Owners of Bail-inable Securities (as such terms are defined in the Indenture), which will in each case be governed by the laws of the Province of Ontario and the Federal laws of Canada applicable therein.

We note that, as of the date of this opinion, a judgment for money in an action based on a Security denominated in a foreign currency or currency unit in a Federal or state court in the United States ordinarily would be enforced in the United States only in United States dollars. The date used to determine the rate of conversion of the foreign currency or currency unit in which a particular Security is denominated into United States dollars will depend upon various factors, including which court renders the judgment. In the case of a Security denominated in a foreign currency, a state court in the State of New York rendering a judgment on such Security would be required under Section 27 of the New York Judiciary Law to render such judgment in the foreign currency in which the Security is denominated, and such judgment would be converted into United States dollars at the exchange rate prevailing on the date of entry of the judgment.

The foregoing opinion is limited to the Federal laws of the United States and the laws of the State of New York, and we are expressing no opinion as to the effect of the laws of any other jurisdiction. In rendering the foregoing opinion, we have assumed that the Bank has been duly incorporated and is an existing corporation in good standing under the laws of Canada, that each Applicable Indenture was or will be duly authorized, executed and delivered by the Bank insofar as the laws of the Provinces of Ontario and Québec and the Federal laws of Canada applicable therein are concerned and that all corporate action by the Bank related to the Securities was or will be duly authorized as a matter of such laws. We understand that you are relying upon the opinion, dated the date hereof, of Norton Rose Fulbright Canada LLP, Canadian counsel for the Bank, that the Bank has been duly incorporated and is an existing corporation in good standing under the laws of Canada, that each Applicable Indenture was or will be duly authorized, executed and delivered by the Bank insofar as the laws of the Provinces of Ontario and Québec and the Federal laws of Canada applicable therein are concerned and that all corporate action by the Bank related to the Securities was or will be duly authorized as a matter of such laws.

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Also, we have relied as to certain factual matters on information obtained from public officials, officers of the Bank and other sources believed by us to be responsible, and we have assumed that each of the indentures relating to the Securities have been or will be duly authorized, executed and delivered by the Trustee thereunder, an assumption which we have not independently verified.

We hereby consent to this filing of this opinion as an exhibit to the Registration Statement and to the references to us under the heading “Validity of Securities” in the prospectus included in 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 Act.

Very truly yours,

/s/ SULLIVAN & CROMWELL LLP