Exhibit 99.1

Alexion Shareholders Approve Increase in Authorized Shares

For Previously Announced Stock Split

Cheshire, Conn., May 12, 2011 – Alexion Pharmaceuticals, Inc. (Nasdaq: ALXN) announced today that its shareholders have approved an increase in the number of authorized shares of common stock from 145 million to 290 million at the Annual Meeting of Stockholders held on May 11, 2011. The increase enables the Company to effect a two-for-one stock split, payable in the form of a 100 percent stock dividend, as approved by Alexion’s Board of Directors in March 2011 and announced at that time. The record date for the stock split is May 2, 2011. Stockholders will receive one additional share for every share they own as of the close of business on May 2, 2011. The additional shares are expected to be distributed after the close of business on May 20, 2011. Reporting of the Alexion share price on a split-adjusted basis will commence on May 23, 2011.

About Alexion

Alexion Pharmaceuticals, Inc. is a biopharmaceutical company focused on serving patients with severe and ultra-rare disorders through the innovation, development and commercialization of life-transforming therapeutic products. Alexion is the global leader in complement inhibition, and has developed and markets Soliris^® (eculizumab) as a treatment for patients with PNH, a debilitating, ultra-rare and life-threatening blood disorder. Soliris is approved in more than 35 countries. Alexion is evaluating other potential indications for Soliris and is pursuing development of other innovative biotechnology product candidates in early stages of development. This press release and further information about Alexion Pharmaceuticals, Inc. can be found at: www.alexionpharma.com.

[ALXN-G]

Contacts:

Alexion Pharmaceuticals, Inc.

Irving Adler, Senior Director, Corporate Communications and Public Policy

203-271-8210

Media

Makovsky & Company

Mark Marmur

609-354-8135

Investors

Rx Communications

Rhonda Chiger

917-322-2569