UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

FORM 8-K

CURRENT REPORT

PURSUANT TO SECTION 13 OR 15(D) OF THE

SECURITIES EXCHANGE ACT OF 1934

Date of report (Date of earliest event reported): May 28, 2010

ALEXION PHARMACEUTICALS, INC.

(Exact name of registrant as specified in its charter)

352 Knotter Drive, Cheshire, Connecticut 06410

(Address of Principal Executive Offices) (Zip Code)

Registrant’s telephone number, including area code: (203) 272-2596

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions (see General Instruction A.2. below):

On May 28, 2010, the Board of Directors of Alexion Pharmaceuticals, Inc. appointed Ms. Ann M. Veneman as a director of Alexion, effective immediately. Most recently, Ms. Veneman served as the Executive Director of the United Nations Children’s Fund, or UNICEF, from May 2005 to April 2010, leading a global organization which supports multiple aspects of child health, nutrition, safety and education in over 150 countries and territories. Prior to joining UNICEF, Ms. Veneman served as Secretary of the U.S. Department of Agriculture from January 2001 to January 2005. Ms. Veneman is expected to serve on two committees of the Board, which will be determined at a later date.

There are no transactions and no proposed transactions between Ms. Veneman (or any member of her immediate family) and Alexion (or any of its subsidiaries), and there is no arrangement or understanding between Ms. Veneman and any other person or entity pursuant to which Ms. Veneman was appointed as a director of Alexion.

As an Alexion director, Ms. Veneman is entitled to receive an annual cash retainer of $57,000, which will be prorated for fiscal year 2010. Upon her election, Ms. Veneman received (a) a grant of stock options to purchase 4,989 shares of Alexion’s common stock, having an exercise price of $50.03, the closing price of Alexion’s common stock on the grant date of May 28, 2010, and (b) a restricted stock award of 2,288 shares of Alexion’s common stock. The inaugural options vest in three equal annual installments over three years and the restricted stock award vests in full on May 28, 2011. Further, in accordance with Alexion’s current director compensation policy, Ms. Veneman is entitled to receive a restricted stock award having a value of $183,000 based on the sixty day trailing average market price of Alexion’s common stock, typically awarded in January of each year and vesting on the first anniversary of the grant date; and a grant of stock options to purchase shares of common stock having a value equivalent to $122,000 calculated using the Black-Scholes model, typically granted upon re-election to the Board in May. Each such stock option has an exercise price equal to the closing price of the stock on the grant date and vests in four equal quarterly installments over one year.

A copy of the press release announcing Ms. Veneman’s appointment is filed as Exhibit 99.1 to this Current Report on Form 8-K.

On June 2, 2010, Alexion and its affiliate Alexion Pharma International Sàrl announced that the launch of Soliris^® (eculizumab) as a treatment for patients with PNH in Japan will begin in the third quarter of 2010, approximately three months earlier than previously expected. In addition, Alexion revised its 2010 financial guidance.

A copy of the press release is filed as Exhibit 99.2 to this Current Report on Form 8-K.

Signature

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.