Exhibit 10

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in this Post-Effective Amendment No. 65 to Registration Statement No. 002-74452 on Form N-1A of our reports each dated February 15, 2013, relating to the financial statements and financial highlights of BlackRock Variable Series Funds, Inc., (the “Company”), comprising the BlackRock Basic Value V.I. Fund, BlackRock Capital Appreciation V.I. Fund, BlackRock Equity Dividend V.I. Fund, BlackRock Global Allocation V.I. Fund, BlackRock Global Opportunities V.I. Fund, BlackRock High Yield V.I. Fund, BlackRock International V.I. Fund, BlackRock Large Cap Core V.I. Fund, BlackRock Large Cap Growth V.I. Fund, BlackRock Large Cap Value V.I. Fund, BlackRock Managed Volatility V.I. Fund (formerly BlackRock Balanced Capital V.I. Fund), BlackRock Money Market V.I. Fund, BlackRock S&P 500 Index V.I. Fund, BlackRock Total Return V.I. Fund, BlackRock U.S. Government Bond V.I. Fund, and BlackRock Value Opportunities V.I. Fund, appearing in the Annual Report on Form N-CSR of the Company for the year ended December 31, 2012.

We also consent to the references to us under the headings “Financial Highlights” and “Funds and Service Providers” in the Prospectuses 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

April 18, 2013