Steve Ballmer, Microsoft chief executive, sent a letter to his Yahoo counterpart, Jerry Yang, withdrawing the offer.
"We regard with particular concern your apparent planning to respond to a 'hostile' bid by pursuing a new arrangement that would involve or lead to the outsourcing to Google of key paid internet search terms offered by Yahoo today," Ballmer said in the letter, which was made public on Saturday.
In a separate letter to Microsoft employees, Ballmer said: "Although the acquisition of Yahoo would have accelerated our ability to deliver on our strategy in advertising and online services, I remain confident that we can achieve our goals without Yahoo.
"We believe the economics demanded by Yahoo do not make sense for us, and it is in the best interests of Microsoft stockholders, employees and other stakeholders to withdraw our proposal."
In turn, Yang issued a statement saying: "With the distraction of Microsoft's unsolicited proposal now behind us, we will be able to focus all of our energies on executing the most important transition in our history so that we can maximize our potential."
Microsoft made an offer for Yahoo on Febuary 1 for $44.6 bn, or $31 per share.
However, a fall in Microsoft's stock price meant the proposal for Yahoo was valued at only $29.62 per share, or just under $41bn.
Ballmer has said the US economic slowdown and volatile stock market had affected Yahoo's value and there were indications that its "search" and "page" view shares had fallen.
Since rejecting Microsoft's bid Yahoo has explored possible alliances with Google, News Corporation's MySpace and Time Warner's AOL, however no viable alternative appears to have emerged so far.