Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in Registration Statements No. 333-180219 and No. 333-193098 on Form S-8 and Registration Statement No. 333-188728 on Form S-3 of M/A-COM Technology Solutions Holdings, Inc. of our report, dated December 13, 2013, relating to the consolidated financial statements and financial statement schedule of Mindspeed Technologies, Inc. and subsidiaries, appearing in the Annual Report on Form 10-K of Mindspeed Technologies, Inc. for the year ended September 27, 2013 and incorporated by reference in this Current Report on Form 8-K/A of M/A-COM Technology Solutions Holdings, Inc.

/s/ Deloitte & Touche LLP

Costa Mesa, California

March 5, 2014