St. Jude Medical (STJ) 8-K/A Completion of Acquisition or Disposition of Assets

Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the Registration Statement No. 333-187405 on Form S-3  and Nos. 333-207341, 333-42945, 333-42668, 333-96697, 333-127381, 333-130180, 333-136398, 333-143090, 333-149440, 333-150839, 333-176200, 333-183158 and 333-183159 on Form S-8 of St. Jude Medical, Inc. of our report dated February 19, 2015, relating to the consolidated financial statements of Thoratec Corporation and subsidiaries, appearing in the Annual Report on Form 10-K of Thoratec Corporation for the year ended January 3, 2015, and incorporated by reference in this Current Report on Form 8-K/A of St. Jude Medical, Inc. dated December 18, 2015.

/s/ DELOITTE & TOUCHE LLP

San Jose, California

December 18, 2015