In a statement, Yahoo acknowledged receipt of the offer and said its board would evaluate the proposal "carefully and promptly."
The deal would pay Yahoo shareholders $31 a share, which represents a 62% premium from where Yahoo stock closed on Thursday.
Microsoft's statement said the offer allows Yahoo shareholders to elect to receive cash or a fixed number of shares of Microsoft common stock, with the software giant's offer consisting of one-half cash and one-half Microsoft common stock.
Shares of Yahoo (YHOO, Fortune 500) shot up nearly 60% in pre-market trading on the news, while shares of Dow component Microsoft (MSFT, Fortune 500) tumbled 5%.
Both Microsoft and Yahoo have fallen far behind rival Google (GOOG, Fortune 500) in the lucrative field of Internet search. Yahoo's earnings and share of the online search market have badly trailed Google.
In a letter it sent to Yahoo's board of directors, Microsoft disclosed it had explored a Microsoft-Yahoo deal a year earlier, only to be rebuffed by Yahoo, which said at that time it was confident of the "potential upside" for Yahoo from operational changes it planned.
"A year has gone by, and the competitive situation has not improved," Microsoft CEO Steve Ballmer wrote.
Yahoo announced Tuesday it would lay off 1,000 employees by mid-February, citing what CEO Jerry Yang described as "headwinds" facing the company. It also reported lower fourth-quarter earnings that still beat Wall Street's now modest expectations for the firm, but it gave a 2008 revenue forecast that disappointed analysts.
