Terms of the deal were not disclosed.
Ford said the sale is expected to close during the second quarter and is subject to closing conditions, including applicable regulatory approvals.
Trident IV is a fund managed by Stone Point Capital.
Ford bought APCO for $180 million in 1999 under former CEO Jacques Nasser as part of a now-abandoned diversification effort away from making autos.
The No. 2 U.S. automaker, facing a deep financial crisis, said in October it wanted to sell the unit, which offers service contracts for all makes of new and used cars through Ford dealers in the United States.
Ford lost a record $12.7 billion last year and expects to burn through $17 billion in cash in the next three year. The company also has its Aston Martin luxury-car division for sale.