The sale will close the chapter on one of the most politically contentious government rescues and turn a profit for taxpayers, a development once seen as inconceivable.
In a statement on Monday, the Treasury said it launched an underwritten public offering for its remaining 234.2 million shares of common stock.
At Monday's closing share price of $33.36, the stake would be worth some $7.81 billion.
Treasury said that the sale, which is expected to price imminently, would be jointly led by Bank of America Merrill Lynch , Citigroup , Deutsche Bank , Goldman Sachs and JPMorgan Chase & Co .
Treasury also said it would continue to hold warrants to buy common stock even after the share offering is complete.
In September 2008, AIG was rescued minutes before it would have been forced to file for bankruptcy protection. The massive bailout ultimately totaled $182.5 billion.
At one point, the government estimated it would never be able to recover all of those funds. But as AIG restructured and returned to viability, it was able to repay the entire rescue plus generate a profit for U.S. taxpayers.
AIG was one of the Treasury Department's most contentious bailouts. U.S. lawmakers began calling for Treasury Secretary Timothy Geithner's resignation after it was revealed that AIG paid $165 million in retention bonuses to employees of a unit that is blamed for destroying the company through investment in risky derivatives.
It prompted Republican lawmaker Charles Grassley to call for AIG executives to resign or commit suicide, though the Iowa senator eventually backtracked from those comments.
The company also funneled over $90 billion of taxpayer money - more than half the funds the government used to rescue AIG - to various European and Wall Street banks, including Goldman Sachs, Deutsche Bank and Barclays Plc .
Robert Benmosche, the former CEO of MetLife , took over as CEO of AIG in August 2009, replacing Edward Liddy, who had been installed by the U.S. government. He will ultimately get the lion's share of the credit for turning the company around and preventing a fire sale of its assets.
In September, Benmosche said the company may be in a position to consider a dividend by next summer.
(Reporting by Timothy Ahmann and Rachelle Younglai in Washington, Ben Berkowitz in Boston and Rick Rothacker in Charlotte; editing by Phil Berlowitz, G Crosse)