Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We have issued our reports dated February 27, 2013, with respect to the consolidated financial statements and internal control over financial reporting included in the Annual Report of HeartWare International, Inc. on Form 10-K for the year ended December 31, 2012. We hereby consent to the incorporation by reference of said reports in the Registration Statements of HeartWare International, Inc. on Forms S-8 (File No. 333-155359, effective November 13, 2008, File No. 333-172424, effective February 24, 2011, and File No. 333-184358, effective October 10, 2012), Forms S-3 (File No. 333-161417, effective December 3, 2009, File No. 333-164004, effective January 20, 2010, and File No. 333-171054, effective December 9, 2010), and Forms S-4 (File No. 333-180988, effective July 3, 2012).

/s/ Grant Thornton LLP

Fort Lauderdale, Florida

February 27, 2013