EXHIBIT (n)

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in this Post-Effective Amendment No. 4 to Registration Statement No. 333-175096on Form N-2 of our report dated August 17, 2015, relating to the financial statements and financial highlights of Eaton Vance Senior Income Trust (the “Trust”), appearing in the Annual Report on Form N-CSR of the Trust for the year ended June 30, 2015, and to the references to us under the headings “Financial Highlights” and “Independent Registered Public Accounting Firm” in the Prospectus and “Independent Registered Public Accounting Firm” and “Financial Statements” in the Statement of Additional Information, which are part of such Registration Statement.

/s/ Deloitte & Touche LLP

Boston, Massachusetts

October 23, 2015