The US company acquired $20.5 billion by floating its AIA branch on the Hong Kong stock market and sold off Alico, its global life insurance subsidiary, to rival firm MetLife for $16.2 billion.
Deemed "too big to fail" by the American government, AIG was rescued with a bailout package at the height of the financial crisis in late 2008.
The government stepped in because the firm could have taken down institutions around the world if it was allowed to collapse.
Chief executive Robert Benmosche said the company is now focused on honouring its pledge to reimburse American taxpayers.
"The initial public offering of AIA last week and the completion of the Alico transaction move us closer to delivering on our promise," he commented.
Part of the money will be used to repay a Federal Reserve Bank of New York credit facility.
By Gary Cooper