GM Chairman and Chief Executive Rick Wagoner will lead the talks, which stem from a proposal by billionaire GM shareholder Kirk Kerkorian.
Japan's Nissan and France-based Renault issued statements saying that both companies looked forward to starting the talks soon.
GM shares were up more than 2 percent after the announcement.
In a teleconference meeting held Friday, the board authorized the company's management to consider the proposal and "weigh the potential benefits of such an alliance in order to assist the board in its decision making," George Fisher, a member of the board, said in a statement.
Kerkorian had been pushing for GM to consider an alliance with Renault and Nissan in an effort to help the world's biggest automaker stage a turnaround and reverse its declining market share.
GM lost $10.6 billion last year but made a $445 million profit in the first quarter of 2006.
GM has made great strides in recent months, with expense savings from 35,000 hourly workers taking early retirements and buyouts, an agreement on health care cost concessions with the United Auto Workers and freezes in health care and pension benefits for salaried workers and executives, spokeswoman Toni Simonetti said.
The company also has new models coming out that should boost sales in the second half of the year, she said.
"General Motors has a lot of experience with different types of alliances and some have provided significant benefits to GM's competitive position and financial strength," Wagoner said in a statement.
"We will enter into discussions with the managements of Renault and Nissan with an open mind — eager to hear their ideas of how an alliance between our companies might work to our mutual benefit. Given the complexity of any potential relationship, it has to be carefully considered on its merits before coming to any conclusion," he said in a statement.
Fisher, retired chairman and CEO of Eastman Kodak Co., said the board will monitor the talks and make sure they serve the best interest of all GM stockholders.
The Nissan and Renault boards each endorsed the discussions after Kerkorian's Tracinda Corp. disclosed the potential alliance in filings June 30 with the Securities and Exchange Commission.
Wagoner said that when the idea of joining with Renault and Nissan was first suggested, he contacted Carlos Ghosn, chief executive of both Renault and Nissan, and the two agreed to meet.
"We periodically receive interesting proposals, and we owe it to the company and its shareholders to explore how they might work, and to objectively weigh the potential benefits and issues that each might present," Wagoner said.
Ghosn is considered the world's most successful auto executive, reports CBS News correspondent Barry Petersen. He runs Renault in France as well as Nissan.
He turned around Nissan seven years ago when it had many of the same problems GM faces today: big losses, poor sales, unhappy workers and a dismal outlook.
"If you bring an attractive product, and you bring a competitive product," Ghosn told Petersen, "there are no other problems you can't solve." However, he says he would decline the chance to run GM because, "I'm not finished with my present challenge."
Some analysts have said that an alliance between GM, Renault and Nisan would mean the end of Wagoner's run at GM.
"I don't think General Motors can be solved from the inside," said Stephen Mader, vice chairman of Christian & Timbers, a New York-based executive search firm, adding that Ghosn had great success turning around Nissan by coming in from the outside.
"You can't get an insider with all of those years with background and affiliations and relationships. You get bogged down in your assumptions about what is possible," he said.
Wagoner, who has been with GM since 1977, is a first-class business leader, but has become bogged down in his perception of GM's realities, Mader said. Ghosn would not be beholden to GM's idiosyncrasies, he said.