Elan shares climbed over 4 percent following the announcement on Friday, which also reiterated the company's intention to make acquisitions with the rest of the $3.25 billion raised from the deal.
Tysabri was by far Elan's most important product, responsible for almost all its revenue and its sale creates uncertainty over the future shape of the company.
"Close to 40 percent of Elan's current market cap could be invested in as yet unknown assets ... we are unlikely to gain the visibility needed to become constructive on the shares until transactions are concluded," said Deutsche Bank analyst Richard Parkes.
Elan is already pursuing potential deals for the next 12-18 months, Chief Executive Kelly Martin told Reuters in an interview this month, which he said may not necessarily be restricted to the firm's past areas of activity.
"By unlocking a portion of the Tysabri asset value ... we have a unique opportunity to reward shareholders, diversify our business and create a highly distinctive business platform upon which to advance to the benefit of shareholders and patients around the world," Martin said on Friday.
Elan, which has operations in Ireland and the United States, indicated last year it would look to return some profit to shareholders from the sale of Tysabri.
The drugmaker has co-marketed Tysabri with Biogen, the larger U.S. company, for 12 years and said it would receive a royalty of 12 percent of Tysabri's global net sales for the first 12 months after the deal is completed.
For Biogen, which plans to pay for the deal using existing cash reserves, the Tysabri deal will add around $0.20 to $0.30 to 2013 earnings per share and continue to be accretive thereafter.
The deal boosts its multiple sclerosis business at a crucial time as it seeks approval for a new pill to treat the debilitating neurological disease.
(Editing by Mark Potter)