Alexion's cash-and-stock offer values Synageva at $225.92 per share—more than double of Synageva closing price of $95.87 on Tuesday.
Synageva's shares were trading at $216 before the bell on Wednesday, while Alexion was down 4 percent at $162.
Makers of drugs that treat rare diseases are attractive because they typically charge hefty premiums for their products.
The deal will give Alexion access to Kanuma—Synageva's treatment for a rare disease called Lysosomal Acid Lipase Deficiency, where build-up of fatty material in the blood and liver causes unexpected complications and some times early death.
Kanuma's marketing application is being reviewed in the United States and Europe.
The deal is the latest in a string of M&As in the health care sector this year.
Recent deals involving rare disease companies include Teva Pharmaceutical's $3.5 billion purchase of Auspex Pharmaceuticals in March and Shire's acquisition of NPS Pharmaceuticals for $5.2 billion in January.
Alexion is offering $115 in cash and 0.6581 of its shares for each share of Synageva.
The deal is expected to add to Alexion's 2018 profit, while allowing $150 million in cost savings in 2017, the companies said in a statement.
Lazard and JPMorgan were Alexion's financial advisers, while Goldman Sachs advised Synageva.
Wachtell Lipton Rosen & Katz is Alexion's legal counsel, while Sullivan & Cromwell and Ropes & Gray are Synageva's legal counsel.