Exhibit 99.1

CHESHIRE, Conn., March 16 /PRNewswire-FirstCall/ — Alexion Pharmaceuticals, Inc. (Nasdaq: ALXN) today announced that Larry L. Mathis, FACHE, has been appointed to the Company’s Board of Directors, bringing the number of board members to eight.

“We are delighted to welcome Larry to our Board of Directors,” said Leonard Bell, M.D., Chief Executive Officer of Alexion. “He is a seasoned, highly respected leader and an internationally recognized consultant on healthcare strategy and policy. His extensive experience and unique insights into the economic and other issues of healthcare delivery will be invaluable as Alexion advances its products to the marketplace.”

Mr. Mathis has held many leadership positions in organizations charged with planning and directing the future of health care delivery in the United States. He has served as Chairman of the Boards of Directors of The Greater Houston Hospital Council, The Texas Hospital Association, The American Hospital Association, and the American College of Healthcare Executives, which conferred its highest lifetime achievement award, the Gold Medal, upon him in 2004. He also served government as a Medicare Prospective Payment Assessment Commissioner and as Chairman of the National Task Force on Health Care Technology Assessment. In 2001, Modern Healthcare named him one of the 25 most influential people in healthcare during the past quarter century.

Since 1998, Mr. Mathis has served as an executive consultant with D. Petersen & Associates providing counsel to select clients on leadership strategies, integrated systems and governance. For the 27 years prior to joining D. Petersen & Associates, Mr. Mathis served in various capacities within The Methodist Health Care System, in Houston, Texas - an organization comprising 16 corporations and 37 hospital affiliates in the U.S. and abroad. From 1997 to 1998, Mr. Mathis served as a consultant to the Chairman of the Board of the System. Prior to that, he was President and Chief Executive Officer, as well as a member of the Board of Directors, from 1983 to 1997.

Under his stewardship, The Methodist Hospital received the “Commitment to Quality Award,” the nation’s foremost award for hospital quality; was named in the 1993 edition of The 100 Best Companies to Work for in America; and was named in The Best Hospitals in America as one of the 64 most exceptional hospitals in the nation.

Mr. Mathis is the author of The Mathis Maxim; Lessons in Leadership, published in 2001 by Leadership Press. He has received numerous professional awards throughout his career including the Medal of Freedom from the U.S. Department of Treasury. He was also named an Honorary Fellow of the American Academy of Medical Administrator and received the Earl M. Collier Award for Distinguished Hospital Administration from the Texas Hospital Association.

Mr. Mathis earned a Master’s degree in Health Administration from Washington University in St. Louis, and a Bachelor of Arts in Social Sciences from Pittsburg State University in Kansas.

“With two drug candidates moving closer to market, I am pleased to join Alexion as it transitions from a research and development company to one that will be addressing the commercial aspects of the healthcare industry,” said Mr. Mathis. “It is in this area where I believe I can provide the most assistance to Alexion. I look forward to working with the entire Board as Alexion advances toward achieving this important goal.”

Alexion is engaged in the discovery and development of therapeutic products aimed at treating patients with a wide array of severe disease states, including cardiovascular and autoimmune disorders, inflammation and cancer. Alexion’s two lead product candidates, pexelizumab and eculizumab, are currently undergoing evaluation in several clinical development programs. Alexion has completed a Phase III clinical study with pexelizumab in CABG patients undergoing cardiopulmonary bypass, and two large Phase II studies with pexelizumab in acute myocardial infarction patients. The Phase III trial and Phase II trials were conducted in collaboration with Procter & Gamble Pharmaceuticals. In addition, eculizumab has completed Phase II clinical trials in rheumatoid arthritis and membranous nephritis, and has completed pilot programs for the treatment of paroxysmal nocturnal hemoglobinuria and dermatomyositis. Alexion is engaged in discovering and developing a pipeline of additional antibody therapeutics targeting severe unmet medical needs, through its wholly owned subsidiary, Alexion Antibody Technologies, Inc. This press release and further information about Alexion Pharmaceuticals, Inc. can be found on the World Wide Web at http://www.alexionpharm.com.

This news release contains forward-looking statements. Such statements are subject to factors that may cause Alexion’s results and plans to differ from those expected, including the results of pre-clinical or clinical studies (including termination or delay in clinical programs), the need for additional research and testing, delays in arranging satisfactory manufacturing capability, inability to acquire funding on timely and satisfactory terms, delays in developing or adverse changes in commercial relationships, the possibility that results of earlier clinical trials are not predictive of safety and efficacy results in later clinical trials, dependence on Procter & Gamble Pharmaceuticals for development and commercialization of pexelizumab, the risk that third parties won’t agree to license any necessary intellectual property to us on reasonable terms, and a variety of other risks set forth from time to time in Alexion’s filings with the Securities and Exchange Commission, including but not limited to the risks discussed in Alexion’s Annual Report on Form 10-K for the year ended July 31, 2003 and in our other filings with the Securities and Exchange Commission. P&GP retains the development rights and the termination rights discussed in Alexion’s Form 10-K referred to above. Alexion does not intend to update any of these forward-looking statements to reflect events or circumstances after the date hereof, except when a duty arises under law.

Contacts:

Alexion Pharmaceuticals, Inc.

Leonard Bell, M.D.

Chief Executive Officer

(203) 272-2596

Euro RSCG Life NRP

Ernie Knewitz (Media)

(212) 845-4253

Rx Communications

Rhonda Chiger (Investors)

(917) 322-2569