Yahoo cut its revenue forecasts earlier this week and said it would have to spend an additional $300m this year trying to revive the company.
It has been struggling in recent years to compete with Google, which has also been a competitor to Microsoft.
In a conference call, Microsoft's Kevin Johnson said that the combination of the two companies would create an entity that could better compete with Google.
"Today the market [for online search and advertising] is increasingly dominated by one player," he said.
Yahoo confirmed that it has received an unsolicited offer and said that its board would evaluate the proposal, "carefully and promptly in the context of Yahoo's strategic plans and pursue the best course of action to maximize long-term value for shareholders."
If Yahoo accepted the offer, competition authorities both in the US and the European Union would be likely to investigate the tie-up.
Yahoo chief executive, Jerry Yang, announced on Tuesday that he intended to lay off 1,000 staff as part of a restructuring plan.
Terry Semel, who stepped down as chief executive last June, also quit as non-executive chairman on Thursday.
Microsoft said that Yahoo shareholders could choose to receive either cash or shares.
Yahoo shares have fallen 46% since reaching a year-high of $34.08 in October. On Friday they closed almost 48% higher.
Microsoft closed 6.6% lower while Google shares fell 8.6%.
"Ultimately this corporate marriage was forced by the rise of Google, which has grown into a serious competitor for both Microsoft as a software company and Yahoo as an internet portal," said Tim Weber, business editor of the BBC News website.
"It is a shotgun marriage, but the person holding the shotgun is Google."
According to its letter to Yahoo, Microsoft attempted to enter talks about a deal a year ago, but was rebuffed because Yahoo was confident about the "potential upside" presented by the reorganisation and operational activities that were being put in place at the time.
"A year has gone by, and the competitive situation has not improved," Microsoft's letter said.
