Microsoft said Friday that it would offer $44.6 billion for Yahoo, the ailing search giant. The surprise offer of $31 a share represents a 62 percent premium to Thursday’s clsoing share price. Yahoo shareholders could elect to receive either cash or stock.

The proposed acquisition, the largest ever by Microsoft, would give some relief to Yahoo’s long-suffering shareholders, who have seen the company’s stock slide nearly 32 percent this year. It would also create the most formidable competitor yet for Google, the search engine giant.

“This proposal represents a compelling value realization event for your shareholders,” Steven A. Ballmer, Microsoft’s chief executive, said in a letter to Yahoo’s board sent Thursday.

Rumors had long persisted that Microsoft might make a bid for the company. In its letter, Microsoft said that the two had held talks early last year, exploring a range of collaborative efforts up to and including a merger. But Yahoo had rebuffed a takeover proposal.

Microsoft’s announcement was unsolicited and its premium unusually high, marking it as an aggressive bid that could turn hostile. Shares in Yahoo jumped nearly 59 percent in pre-market trading Friday, reflecting investors’ apparent wild enthusiasm for the deal.

Yahoo, one of the early Internet giants, remains one of the biggest companies on the Web. Its main site attracts the largest amount of traffic of any Web site, and many of its services, like Yahoo Mail, are immensely popular as well.

Microsoft has sought to improve its distant third position by making a series of acquisitions, notably by buying the online advertising company aQuantive for $6 billion.

But Yahoo has floundered as the company failed to take online advertising revenue from Google. It ousted Terry Semel as its chief executive last June but remained as nonexecutive chairman. (He is leaving the board, the company said Friday.)

Yahoo reinstalled a co-founder, Jerry Yang, at the top on an interim basis; he promised to begin a turnaround within 100 days.
But the company has not improved appreciably since then. It reported a drop in quarterly profits on Tuesday and said it would cut 1,000 jobs.

One potential roadblock to a Microsoft-Yahoo merger would be antitrust concerns, especially from the European Union. A spokesman for Neelie Kroes, the E.U. Competition Commissioner, declined to comment on Microsoft’s proposal, Reuters reported.