Exhibit 99.1

ALEXION REPORTS FIRST QUARTER 2011 RESULTS

— Soliris^® (eculizumab) Net Product Sales Increased 41% to $166.1 Million —

— Continued Steady Growth in Core Territories: US, Western Europe and Japan —

— US and EU Marketing Applications Submitted for Soliris as a Treatment for Patients with aHUS —

First Quarter 2011 Financial Highlights:

CHESHIRE, Conn., April 21, 2011 — Alexion Pharmaceuticals, Inc. (NASDAQ: ALXN) today announced financial results for the three months ended March 31, 2011. Alexion Pharmaceuticals, Inc. (“Alexion” or, the “Company”) reported net product sales of Soliris^® (eculizumab) of $166.1 million, reflecting steady additions of new patients, compared to $117.6 million for the same period in 2010.

Soliris, approved in the US (2007), European Union (2007) and Japan (2010), is the only drug specifically indicated for the treatment of patients with paroxysmal nocturnal hemoglobinuria (PNH), a rare, debilitating and life-threatening blood disease.

Historically, Alexion’s non-GAAP operating results have been equal to GAAP operating results less both the impact of share-based compensation and taxes that are not payable in cash (non-cash taxes). With the completion of two acquisitions in the quarter, Alexion’s non-GAAP operating results will now also exclude amortization of acquired intangible assets and costs associated with acquisitions. The following summary table is provided for investors’ convenience:

(in thousands of US dollars, except per-share data)

First Quarter Non-GAAP Financial Results:

The Company reported non-GAAP net income of $56.3 million, or $0.59 per share, for the first quarter of 2011, compared to non-GAAP net income of $34.6 million, or $0.37 per share, in the first quarter of 2010.

Alexion’s non-GAAP operating expenses for Q1 2011 were $85.9 million, compared to $65.2 million

for Q1 2010. Non-GAAP research and development (R&D) expenses for Q1 2011 were $28.1 million, compared to $20.3 million for Q1 2010. The increase in R&D expenses primarily reflected the expansion of the Company’s clinical trial programs. Non-GAAP selling, general and administrative (SG&A) expenses for Q1 2011 were $57.8 million, compared to $44.9 million for Q1 2010. The increase in non-GAAP SG&A expenses primarily reflected costs associated with the expansion of the Company’s commercial operations in new geographies.

First Quarter GAAP Financial Results:

Alexion reported GAAP net income of $26.8 million, or $0.28 per share, for Q1 2011, including a negative after-tax impact of $6.9 million, or $0.07 per share, from costs related to the Taligen Therapeutics and Orphatec Pharmaceuticals acquisitions during the quarter, compared to Q1 2010 GAAP net income of $20.9 million, or $0.23 per share.

On a GAAP basis, operating expenses for Q1 2011 were $106.7 million, including $10.0 million of acquisition-related costs, compared to $73.0 million for Q1 2010. GAAP R&D expenses for Q1 2011 were $30.8 million, compared to $22.4 million for Q1 2010. GAAP SG&A expenses were $65.9 million for Q1 2011, compared to $50.6 million for Q1 2010.

Balance Sheet:

As of March 31, 2011, the Company had $348.8 million in cash, cash equivalents and marketable securities, compared to $361.6 million at the end of 2010. The amount outstanding at the end of the quarter reflected outflows of approximately $114 million associated with the Taligen Therapeutics and Orphatec Pharmaceuticals acquisitions and inflows of $60 million in short-term borrowing during the first quarter.

“In the early months of 2011, we achieved steady growth in serving patients with PNH in our core territories, and started laying the initial groundwork for expanding into new major countries. At the same time, we have reached a key milestone in our aHUS program with our US and EU regulatory submissions,” said Leonard Bell, M.D., Chief Executive Officer of Alexion. “As we look ahead in 2011, we expect continued growth in our PNH operations and notable progress toward serving patients with other severe and ultra-rare disorders through the accelerated development of our expanded pipeline portfolio.”

Research and Development Programs:

aHUS Submissions

In early April, the Company announced that it has submitted marketing applications to the US Food and Drug Administration (FDA) and the European Medicines Agency (EMA) for Soliris as a treatment for patients with atypical Hemolytic Uremic Syndrome (aHUS). Both the US and EU submissions include the positive data from the two 26-week Phase 2 studies of Soliris as a treatment for adult and adolescent patients with aHUS.

Transplant: Acute Humoral Kidney Rejection (AHR)

Eculizumab is being investigated as a treatment for patients undergoing kidney transplant who are at elevated risk of antibody mediated rejection, also known as acute humoral rejection (AHR). Alexion today announced that it has recently concluded successful discussions with regulators regarding the clinical protocols for two global, company-sponsored controlled clinical trials evaluating eculizumab to prevent AHR in patients undergoing kidney transplant in living- or deceased-donor settings. The Company is preparing to initiate these studies later this year. Alexion continues to support investigator-initiated studies in elevated-risk kidney transplantation in the US and Australia.

New Product Development

Alexion has established a Translational Medicine Center of Excellence in Cambridge, Massachusetts to more rapidly move early-stage drug candidates into clinical trials. Beyond eculizumab, the Company is initially focused on four unique and innovative drug candidates. Alexion has accelerated the clinical development of TT30, a specific inhibitor of the alternative complement pathway with a mechanism of action distinct from Soliris, and expects to initiate clinical development of TT30 in 2011. The Company is also focused on accelerating the development of its cPMP replacement therapy for patients with molybdenum cofactor deficiency (MoCD) Type A. In addition, a novel anti-inflammatory antibody is expected to enter clinical trials in a rare and life-threatening disorder in the second half of this year. Finally, the Company expects to initiate a clinical trial of samalizumab in patients with a rare, solid tumor later this year.

2011 Financial Guidance:

Earlier this month, Alexion updated its 2011 revenue guidance, from the previously announced range of $715 to $735 million, now to the higher range of $720 to $740 million. The upward revision in revenue guidance takes into account continued global growth of Soliris for PNH, and the potential for an earlier than previously expected launch of Soliris for aHUS in the US. The earlier US launch could occur if the regulatory submission is granted priority review by the FDA, and if a positive decision is then received, making a launch in the US possible late in the fourth quarter of 2011.

Other items of previously announced 2011 guidance are being reiterated at this time.

Conference Call/Web Cast Information:

Alexion will host a conference call/webcast to discuss matters mentioned in this release. The call is scheduled for today, April 21, 2011, at 10:00 a.m., Eastern Time. To participate in this call, dial 888-297-9007 (USA) or 719-325-2212 (International), confirmation code 3335096 shortly before 10:00 a.m., Eastern Time. A replay of the call will be available for a limited period following the call, beginning at 1:00 p.m. Eastern Time. The replay number is 888-203-1112 (USA) or 719-457-0820 (International). The audio webcast can be accessed at www.alexionpharma.com.

About Soliris:

Soliris is a first-in-class terminal complement inhibitor developed from the laboratory through regulatory approval and commercialization by Alexion. Soliris has been approved in the US, European Union, Japan and other territories as the first treatment for patients with PNH, an ultra-rare, debilitating and life-threatening blood disorder defined by chronic uncontrolled complement activation which causes chronic red blood cell destruction (hemolysis), leading to blood clots, organ failure, and shortened survival. Prior to these approvals, there were no therapies specifically available for the treatment of patients with PNH. Soliris (eculizumab) is not approved for the treatment of aHUS or other indications other than PNH. Alexion’s breakthrough approach to complement inhibition has received some of the pharmaceutical industry’s highest honors: the 2008 Prix Galien USA Award for Best Biotechnology Product with broad implications for future biomedical research and the 2009 Prix Galien France Award in the category of Drugs for Rare Diseases. More information on Soliris is available at www.soliris.net.

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.

This press release includes certain non-GAAP financial measures that involve adjustments to GAAP figures. Alexion believes that these non-GAAP financial measures, when considered together with the GAAP figures, can enhance an overall understanding of Alexion’s past financial performance and its prospects for the future. The non-GAAP financial measures are included with the intent of providing both management and investors with a more complete understanding of underlying operational results and trends. In addition, these non-GAAP financial measures are among the primary indicators Alexion management uses for planning and forecasting purposes and measuring the Company’s performance. These non-GAAP financial measures are not intended to be considered in isolation or as a substitute for GAAP figures. A reconciliation of the GAAP to non-GAAP figures is included in this press release.

[ALXN-E]

This news release contains forward-looking statements, including statements related to guidance regarding anticipated financial results for 2011, assessment of the Company’s financial position and commercialization efforts, medical benefits and commercial potential for Soliris for PNH and aHUS and other potential indications, expansion of clinical and commercial operations to additional countries, potential of Alexion’s complement-inhibition technology and other technologies; plans for clinical programs for each of our product candidates; plans for recently acquired companies and programs; progress in developing commercial infrastructure, and interest and acceptance regarding Soliris in the patient, physician and payor communities. Forward-looking statements are subject to factors that may cause Alexion’s results and plans to differ from those expected, including for example, decisions of regulatory authorities regarding marketing approval or material limitations on the marketing of Soliris for PNH and aHUS and other potential indications, delays in arranging satisfactory manufacturing capabilities and establishing commercial infrastructure, the possibility that results of clinical trials are not predictive of safety and efficacy results of Soliris in broader patient populations in the disease studied or other diseases, the risk that recent acquisitions will not

result in short-term or long-term benefits, risks related to the integration of the operations of Taligen into Alexion, the possibility that initial results of commercialization are not predictive of future rates of adoption of Soliris in PNH, aHUS or other diseases, the risk that third parties will not agree to license any necessary intellectual property to Alexion on reasonable terms or at all, the risk that third party payors (including governmental agencies) will not reimburse for the use of Soliris at acceptable rates or at all, the risk that estimates regarding the number of patients with PNH, aHUS or other disorders is inaccurate, 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 period ended December 31, 2010 and in our other filings with the Securities and Exchange Commission. 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.

(Tables Follow)

ALEXION PHARMACEUTICALS, INC.

CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS

(in thousands, except per share amounts)

(unaudited)

ALEXION PHARMACEUTICALS, INC.

CONDENSED CONSOLIDATED BALANCE SHEETS

(in thousands)

(unaudited)