EXHIBIT 23.2

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in Registration Statement (File No. 333-189560) on Form S-8 of bluebird bio, Inc. of our report dated March 21, 2013 (June 3, 2013 for Reverse Stock Split paragraph in Note 2), relating to our audit of the consolidated financial statements for the year ended December 31, 2011, which appears in this Annual Report on Form 10-K of bluebird bio, Inc. for the year ended December 31, 2013.

/s/ McGladrey LLP

Boston, Massachusetts

March 5, 2014