GM said in a statement that its board had made the decision because of "an improving business environment for GM over the past few months".
GM had agreed to sell Opel and Vauxhall to Canadian car parts firm Magna. It said it would now be seeking aid for Opel from the German government and other European states. 'Restructuring' GM added that it had come to its decision because of the importance of Opel and Vauxhall to its global strategy.
It said it would now "initiate a restructuring of its European operations in earnest".
"We understand... it was in GM's best interests to retain Opel," said Magna co-chief executive officer Siegfried Wolf. "We will continue to support Opel and GM in the challenges ahead."
But there was anger in Germany, where the planned sale of Opel had been dragging on for months and the German government had pledged Magna US$6.7 billion in financial aid.
After the decision was announced, German Economy Minister Rainer Bruederle called GM's behaviour "totally unacceptable", while Christine Lieberknecht, the premier of Thuringia state, which hosts an Opel plant, called the decision a "low blow".
Government spokesman Ulrich Wilhelm said Berlin regretted the decision, adding that it wanted GM to repay 1.5 billion euros in bridge financing extended by German banks.
GM first said in March that it wished to offload Opel and Vauxhall, before finally agreeing to sell to Magna in September.
The US giant's decision to sell its main European business was made after it was forced to announce a group-wide loss of US$30.9 billion for 2008, after its sales plummeted in the global recession.
However, aided by financial support from the US government, and a brief period in US bankruptcy protection in June and July of this year, GM has since managed to turn around its fortunes.
On Tuesday, GM said its US sales had risen in September for the first time in almost two years. It is in this context that it now wishes to hold onto Opel and Vauxhall.
Car analysts said they were not too surprised by GM's announcement.
With BBC Worldwide