SAN FRANCISCO  Microsoft said Friday that it has made an offer to buy Yahoo for about $44.6 billion, or $31 a share, in a mix of cash and stock.

The offer represents a 62 percent premium over Yahoo’s closing stock price of $19.18 on Thursday.

If consummated, the deal would redraw the competitive landscape of the Internet consumer services business, where both Microsoft and Yahoo have struggled to compete with Google.

Microsoft said the combination of the two companies would create efficiencies that would save approximately $1 billion annually. The software giant also said that it has an integration plan to include employees of both companies and intends to offer incentives to retain Yahoo employees.

"We have great respect for Yahoo!, and together we can offer an increasingly exciting set of solutions for consumers, publishers and advertisers while becoming better positioned to compete in the online services market," said Steven A. Ballmer, Microsoft’s chief executive, in a statement.