About 80,000 square feet of the leased space is hangar bays, and the rest is office, training rooms and other uses, said FedEx spokeswoman Paula Bosler.
FedEx will use the ATA space to maintain all but its largest airplane, the MD-11. Jobs will not be created immediately, but might in the long term, she said.
About 250 of the 4,250 FedEx employees at the airport work in a FedEx maintenance hangar close by the former ATA site.
Summit Realty Group brokered the lease.
The building, at 7661 N. Perimeter Road has 150,000 square feet of hangar space and 120,000 square feet of office space.
ATA began outsourcing aircraft maintenance after its 2004 Chapter 11 bankruptcy filing.
Rolls-Royce leased 40,000 square feet of the office space; the remaining 80,000 square feet of offices are vacant.
The building was acquired in June 2006 from Regions Bank by PK Ind Partners LLC, which includes developer Paul Kite and real estate broker John Bales.