Alexion Pharmaceuticals (ALXN) 8-K Alexion Pharmaceuticals Announces Completion of Common Stock Offering

Exhibit 99.1

Contacts:
Alexion Pharmaceuticals, Inc.	Rx Communications	Noonan/Russo
Leonard Bell, M.D.	Rhonda Chiger (Investors)	Emily Poe (Media)
Chief Executive Officer	(917) 322-2569	(212) 845-4266
(203) 272-2596

Alexion Pharmaceuticals Announces Completion of Common Stock Offering

CHESHIRE, Conn., August 17, 2005 — Alexion Pharmaceuticals, Inc. (Nasdaq: ALXN) announced today that it completed its previously announced public offering of 2,500,000 shares of its common stock. The gross proceeds, before discounts, commissions and expenses, of the offering are approximately $66,875,000. Alexion intends to use the proceeds from this offering for general corporate purposes.

This press release does not constitute an offer to sell or the solicitation of an offer to buy any of these securities. A shelf registration statement relating to the shares of common stock has previously been filed with and declared effective by the Securities and Exchange Commission. This offering of shares of common stock was made only by means of a prospectus supplement and accompanying prospectus. Morgan Stanley & Co. Incorporated acted as underwriter for the offering. Copies of the prospectus supplement and the accompanying prospectus may be obtained from Morgan Stanley, attention Prospectus Delivery Department: 1585 Broadway, New York, New York 10036-8200, (212) 761-6775.

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