GM received about $50 billion from the U.S. Treasury as part of its 2009 bankruptcy restructuring in 2009 under the Troubled Asset Relief Program (TARP).
The deal will raise the proceeds Treasury has recovered to $28.6 billion. That leaves $20.9 billion left on the original bailout amount, meaning the government would have to sell its remaining shares at an average price of $69.72 to break even.
The government bailed out GM and Chrysler Group in a move to protect jobs — a number it put at more than 1 million.
"TARP was always meant to be a temporary, emergency program. The government should not be in the business of owning stakes in private companies for an indefinite period of time," Assistant Secretary for Financial Stability Timothy Massad said in a statement.
"Moving to exit our investment in GM within the next 12 to 15 months is consistent with our dual goals of winding down TARP as soon as practicable and protecting taxpayer interests."
After the buyback, Treasury will still own a stake of about 19 percent, down from about 26 percent currently. Ammann said GM will not buy more shares directly from Treasury after this buyback is completed.
Ammann said the move and resulting Treasury plans will remove an "overhang" on the stock that has hurt sales and bring an "element of closure" to the bailout.
GM will end the year with estimated liquidity of about $38 billion, even after the deal, he said. That will add to earnings per share by reducing the number of outstanding shares by about 11 percent.
GM will take a charge of about $400 million in the fourth quarter tied to the buyback.
In addition, Treasury has agreed to relinquish certain governance rights, including required levels of U.S. manufacturing and barring the purchase of corporate jets, Ammann said. Senior executive payment caps under TARP remain in place.