The deal will comprise of $25 billion in cash, $8.5 billion in equity and equity securities and $2 billion worth of preferred stock in Prudential.
AIG will then use $25 billion of the amount received from the AIA sale to repay some of its debts to the Federal Reserve Bank of New York.
The firm intends to gradually cash in the remaining $10.5 billion over time â money that will also be put towards reducing the amount it owes to the Federal Reserve.
Bob Benmosche, chief executive officer and president of AIG, said: "We decided that a sale to Prudential enables AIG to realize value on a faster track to repay US taxpayers.
"This transaction, the most significant milestone to date in our ongoing effort to repay taxpayers, also gives us greater flexibility to move forward with AIG's restructuring and focus on enhancing the value of our key insurance businesses."
He added that the deal will allow Prudential to create a "powerhouse" in the Asian life insurance industry â one of the fastest-growing markets in the world.
The deal, which has already been approved by the board of directors at both Prudential and AIG, is set to go through by the end of this year â subject to approval from regulators and Prudential shareholders.
If it goes ahead, Prudential will take control of a company with more than 23,000 employees and 23 million customers across 15 markets in the region.
Last week, Gerry Pasciucco, who was bought into AIG to oversee the dismantling of its Financial Products unit, told the Financial Times that the company had changed its plans to sell off its entire derivatives portfolio.
Instead, it will keep around 25 per cent of the stock in an attempt to benefit from improving credit markets.
By Asim Shah