CHICAGO — General Motors Co. will purchase 200 million shares of GM common stock held by the U.S. Department of the Treasury for $5.5 billion, or $27.50 per share, it said Wednesday, noting that the transaction will close by year-end.

The share buyback is part of the Treasury’s plan to fully exit its entire holding—which stands at 500.1 million shares—of GM stock within 12 to 15 months, subject to market conditions. The Treasury intends to begin its disposition of its remaining shares as soon as January, consistent with a pre-arranged written trading plan, it said. The move is part of the agency’s continuing efforts to wind down its investments in the Troubled Asset Relief Program (TARP).

“The auto industry rescue helped save more than a million jobs during a severe economic crisis, but TARP was always meant to be a temporary, emergency program. The government should not own stakes in private companies for an indefinite period of time,” Timothy G. Massad, the Treasury’s assistant secretary for financial stability, said.

In 2008 and 2009, the agency invested $49.5 billion to help stabilize and restructure GM. Including GM’s current stock purchase from the Treasury, the government has recovered more than $28.7 billion of that initial investment.

The share purchase will help to “further remove the perception of government ownership of GM among customers, and demonstrates confidence in GM’s progress,” Dan Akerson, the Detroit-based automaker’s chairman and chief executive officer, said Wednesday.

The industry in general, and GM in particular, have rebounded sharply since the rescue. Since 2008, GM has outlined investments or spent $7.3 billion in the United States and created or retained more than 20,000 jobs.