Drilling in the Telemark field, located in 4,000ft of water, was stalled following the Deepwater Horizon oil spill in 2009.
ATP chief financial officer Al Reese and president Leland Tate said that production from the field was expected to start this year.
Along with the Telemark well, the company has also received permits to complete its Clipper well in the West Green Canyon.
Tate also said that ATP had applied for a permit to drill a fourth Telemark well and expects the approval in 60 days.
In addition, the company also plans to apply for permits to drill three additional deepwater wells through 2012.