GM has been trying to sell Saab since January.
GM says it has failed to sell its Swedish car brand Saab and will begin "an orderly wind-down of Saab operations".
GM had been in talks with the Dutch speciality car maker Spyker over a sale. Talks with Sweden's Koenigsegg also fell through earlier this year.
"We regret that we are not able to complete this transaction with Spyker Cars," said GM Europe boss Nick Reilly.
GM has been trying to sell Saab as part of its turnaround plans since January.
Jorn Madslien, Business reporter, BBC News
It is the end of the road for Saab, the car that emerged from a company making fighter jets.
When its owner GM bought Saab, it was seen as a brand that could become the US automotive group's European luxury brand.
But the quirky cars did not attract a broad enough following, so it failed to make money.
GM's solution was to cut costs by sharing ever more parts with Opel while, at the same time, toning down their design.
Such moves alienated traditional Saab customers without gaining new ones.
New product development ground to a halt and in the end, there was simply not enough left of Saab to make it worth preserving.
Mr Reilly added that all debts would be paid and that the winding-down would be "an orderly process".
On a conference call, GM vice-president John Smith said it became clear that there were serious problems with the Spyker talks that could not be resolved.
He said: "We reached a point of impasse, we decided to deal with it and move on."
A statement from the firm said that Saab would continue to honour all warranties, while providing service and spare parts to current Saab owners around the world.
Last week, Saab agreed a deal with Beijing Automotive to sell it some of Saab's technology. That deal will not be affected by the latest announcement.
Saab employs 3,400 people in Sweden and GM estimates 8,000 people will suffer indirectly.
Sweden's government said it was sad news but that it would not step in to save Saab.
THE HISTORY OF SAAB
1937: Saab founded as aircraft maker
1946: Starts making cars
1969: Merges with Scania-Vabis
1990: Car division splits from aircraft business. GM and Investor AB take 50% stake
2000: GM takes 100% ownership
Jan 2009: GM announces talks to sell Saab
Aug 2009: Koenigsegg agrees terms to buy Saab.
Nov 2009: Koenigsegg pulls out of talks.
1 Dec 2009: GM says will consider offers until end of December
18 Dec 2009: GM announces the winding down of Saab
"It is very dismal. Very sad news for all of the employees and it comes at the worst possible time", the Enterprise Minister Maud Olofsson told the Swedish news agency TT.
She has called a meeting to discuss the situation with unions on Monday.
"I don't think GM really knows how the wind-down is going to take place, but GM has to take its responsibility," she said.
"The most important thing right now is to take care of the employees and the future, how to make the most of their know-how," she added.
Last year, Saab lost 3bn kronor (£255m; $412m). It has not made a profit since 2001 and made up 1.1% of GM's global sales.
"This has been 20 years in the making. At one point, Saab had cachet, but it just didn't update its models fast enough," said Michael Tyndall, auto specialist at Nomura. "This just shows that the industry moves on and if you don't invest, you don't do well."
Saab was just about to replace its 9-5 model after more than a decade on the market. Most car companies bring out a new model every five or six years.
GM said its focus would remain on its four core brands - Buick, Cadillac, Chevrolet and GMC - as well as its European business Opel.
GM pledged to become a leaner company when it emerged from bankruptcy protection in July this year. It had been hit by a sharp slump in sales - partly because of the financial crisis, but also because of stiff competition from Japanese rivals.
The company is now 62%-owned by the US government.