The settlement is likely to be one of the biggest in US history, following a class action lawsuit led by three Ohio pension funds.
They alleged that AIG had engaged in stock price manipulation, anti-competitive behaviour and accounting fraud between 1999 and 2005.
That, they say, resulted in shareholders losing millions.
The court now needs to give its approval before payments can be made.
A first payment of $175m is scheduled within days of the court’s approval, however, while AIG is expected to raise the further $550m though the issuing of new shares.
AIG is now 80% owned by the US government following a massive bailout of the company at the height of the financial crisis.
Ohio Attorney General Richard Cordray, who represented the Ohio funds, said total payouts from AIG to shareholders would now total $1bn, including previous settlements.
AIG said it was “pleased to have resolved this matter”, adding that it could now focus on paying back taxpayers the $182bn used to rescue it.