The U.S. will sell its remaining shares in General Motors Co. by the end of the year, closing an extraordinary chapter in the country's economic history and clearing the way for the No. 1 U.S. auto maker to begin paying shareholders and selecting its next chief executive.

Sales of the remaining 2.2% stake—31.1 million shares—will begin immediately, the Treasury Department said on Thursday. No timetable was provided—the Treasury said the sale would take place depending on market conditions. It previously had indicated it would complete its GM stock sales in 2014.

The Treasury initially had a 61% ownership stake after a controversial move by the Obama administration to bail out GM and Chrysler Group LLC and lead them separately through quick bankruptcy reorganizations in 2009.