After months of braggadocio, proclamations, and posturing, Microsoft has decided on Saturday to throw in the towel and drop its bid for Yahoo.

CEO Steve Ballmer notified Yahoo CEO Jerry Yang via a letter on Saturday. The company posted the text of the letter on its Web site this evening.

"Despite our best efforts, including raising our bid by roughly $5 billion, Yahoo has not moved toward accepting our offer. After careful consideration, 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," said Ballmer.

Microsoft (NASDAQ: MSFT) first dropped the bomb that it intended to buy out Yahoo (NASDAQ: YHOO), the number two competitor in the online search business, in late January. At the time of the initial offer, the deal was worth roughly $44.6 billion – half in stock and half in cash.

Yang and other Yahoo executives immediately sprang into action in an apparent move to block a takeover.

Now, after three months of wrangling and finagling, with Yahoo seeking almost any partner but Microsoft, Ballmer and company finally threw up their collective hands.

"I first called you with our offer on January 31 because I believed that a combination of our two companies would have created real value for our respective shareholders and would have provided consumers, publishers, and advertisers with greater innovation and choice in the marketplace," Ballmer's letter said.

As time went on and the price of both companies' stocks fell, many analysts had expected Ballmer to launch a hostile takeover, including the possibility of submitting its own slate for Yahoo's board of directors. That now will not happen.

In a prompt response to the withdrawal of the bid, Yahoo issued a statement reiterating its long-held position that Microsoft's offer shortsighted the company's brand value and its prospects for future growth.

"From the beginning of this process," wrote Yahoo Chairman Roy Bostock, Yahoo "has been steadfast in our belief that Microsoft's offer undervalued the company, and we are pleased that so many of our shareholders joined us in expressing that view."

Looking forward, Yang added that "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."

Microsoft runs a far third place in the online search arena, well behind both Google (NASDAQ: GOOG) and Yahoo. The company had sought to buy Yahoo to create a combined search entity capable of challenging Google's global dominance.

In his letter, Ballmer also enumerated several moves Yahoo has made in the past three months that undermine the reasons Microsoft wanted Yahoo in the first place.

"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. In our view, such an arrangement with the dominant search provider would make an acquisition of Yahoo! undesirable to us," Ballmer said.