"We will work closely with the Saab organisation to wind down the business in an orderly and responsible manner. This is not a bankruptcy or forced liquidation process."
The failed talks followed the withdrawal of a bid last month from Koenigsegg Group AB, a Swedish sportscar maker.
Saab employs at least 3,400 people in Sweden and sold more than 93,000 cars worldwide in 2008.
'Dismal, sad news'
Up to 15,000 jobs could disappear when Saab is shutdown, including those of suppliers and subcontractors.
"GM owns Saab and GM could have done much more for Saab over the years"
Sweden's enterprise minister
Maud Olofsson, the Swedish enterprise minister, said that GM could have done more to save the marque.
"GM owns Saab and GM could have done much more for Saab over the years," he told a news conference in Saab's hometown of Trollhaettan.
"It is very dismal, very sad news for all of the employees and it comes at the worst possible time."
The US automaker said that it would satisfy Saab's debts, including supplier payments, and would continue to honour warranties and provide parts to Saab owners around the world.
GM said the move to end Saab operations was among "some very difficult but necessary business decisions".
The US auto giant is trying to restore profitability after a massive bankruptcy restructuring aided by the US and Canadian governments.
The company has previously decided to discontinue its Saturn and Pontiac brands in the US and has reached a deal to sell its Hummer brand to a Chinese buyer.
The focus on core brands "will enable the company to devote more engineering and marketing resources to each brand and model," GM said.
Chinese state-owned Beijing Automotive Industry Holdings will acquire the technology for Saab's 9-3 and 9-5 car models, turbine engines and gearboxes, allowing the Chinese firm to develop its own-brand cars using the Swedish carmaker's technology.
Under GM's stewardship, spanning almost two decades, Saab rarely posted a profit and last year lost an equivalent of $341 million at the time.
Saab's history as an automaker dates back to the 1940s when the first cars were produced by the Swedish aircraft maker Svenska Aeroplan Aktiebolaget or SAAB.
GM acquired Saab Automobile in 1990.