Biogen Idec Inc. has agreed to make an upfront payment of $3.2 billion as well as future contingent payments to acquire the full rights to the multiple sclerosis drug Tysabri from its Irish partner Elan Corp. Plc, which owns 50 percent, Biogen Idec said.

The deal would give the Weston biotech complete control of Tysabri, its fastest growing product, which many doctors and patients view as one of the most effective therapies now on the market in treating MS. The autoimmune disease affects the brain and central nervous system of an estimated 400,000 people in the United States and 2.5 million globally.