AIG, which was nearly wiped out by derivative bets in the financial crisis, has been trying for at least four years to sell International Lease Finance Corp (ILFC) to help repay the costs of a 2008 US government bailout.
The deal includes $3 billion in cash and 97.56 million newly issued AerCap common shares, AIG said on Monday. The sale will give AIG a 46% stake in AerCap.
AIG shares rose 1.5% to $50.48 before the bell on Monday. AerCap shares rose 8.7% to $27.10.
Netherlands-based AerCap, which buys aircraft and rents them to airlines, will vie with General Electric's Gecas unit as the world's largest aircraft-leasing company by fleet size after the deal.
ILFC will become a wholly owned subsidiary of New York-listed AerCap. AIG will be entitled to nominate two directors for election to the board of AerCap.
AIG said in December 2012 that it had reached a deal to sell up to 90 percent of ILFC to a group of investors based mainly in China for $4.7 billion, but the deal never went through.
AIG CEO Robert Benmosche said in November that the insurer hoped to decide on a sale or an initial public offering of ILFC in the fourth quarter.
The transaction is expected to close in the second quarter of 2014, AIG said on Monday. UBS was the financial adviser to AerCap while Goldman Sachs was the financial adviser to AerCaps board.