The sale marks the beginning of the end of a drawn-out process fraught with political wrangling over the past year.
AIG has been trying to sell the unit for some 15 months as part of its plans to help pay back the US government for its $180bn bailout, but regulatory issues have dogged the sale process and might yet delay it further.
The buyer group, called Ruen Chen Investment and comprising Ruentex Industries and shoe maker Pou Chen, has signed a deal for the 97.57 per cent of Nan Shan that is for sale, Ruentex said in a statement to the Taiwan stock exchange.
"Ruen Chen offers strong operational and funding capabilities and possesses a clear ability to satisfy the strict criteria that governed AIG's bid review process," said Robert Benmosche, AIG president and chief executive, in a separate statement.
AIG had a deal worth $2.15bn last year blocked by the regulator, citing concerns about the previous bidders' industry experience.
That forced AIG to put the asset back on sale and prompted Benmosche to personally visit the regulators in December to discuss the sale.
Sources have previously told Reuters that Ruentex, a major player in the hypermarket business in China and Taiwan, may not meet all of the five criteria the regulator has laid down for a buyer.
"The regulators' criteria are subject to interpretation. Hence, there is still some uncertainty about this deal going through," said Sally Yim, senior analyst at the financial institutions group at Moody's Investors Service, adding that AIG is likely to have reviewed the bid carefully so would feel confident about getting it past the regulators.