Alexion Pharmaceuticals (ALXN) 10-K 2009 FY Annual report

Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in the Registration Statements on Form S-3 (No. 333-127471, 333-123828, 333-91265, 333-29617, 333-41397, 333-47645, 333-89343, 333-36738, 333-52886 and 333-59702) and Form S-8 (No. 333-146319, 333-139600, 333-123212, 333-119749, 333-24863, 333-52856, 333-69478, 333-71879, 333-71985, 333-106854 and 333-153612) of Alexion Pharmaceuticals, Inc. of our report dated February 23, 2010 relating to the financial statements and the effectiveness of internal control over financial reporting, which appears in this Form 10-K.

Hartford, Connecticut

February 23, 2010