American International Group Inc. agreed to wind down its $182.3 billion bailout by converting the Treasury Department stake into common shares for sale, a step toward independence for the insurer whose near collapse two years ago threatened the global economy. The company gained 3.4 percent in New York trading.

Treasury will swap its preferred stake of $49.1 billion for 1.66 billion shares of common stock and then sell the holdings in the open market, AIG said today in a statement. The Treasury investment will break even if shares are sold at about $29 each. The sales will happen in phases over 18 months to two years, said a person with direct knowledge of the plan who declined to be identified because the schedule isn’t public.

AIG, once the world’s largest insurer, turned over a majority stake to the government in exchange for a rescue that swelled to $182.3 billion. Federal Reserve Chairman Ben S. Bernanke has said the bailout, a day after the September 2008 failure of Lehman Brothers Holdings Inc., made him “more angry” than any other episode in the financial crisis.