The deal is pending a physical. Free agency opens Wednesday at 4 p.m. ET.
McCoy made six consecutive Pro Bowls from 2012-17. He spent the first nine years of his career with the Tampa Bay Buccaneers before joining the Carolina Panthers for the 2019 season. He played in all 16 games and recorded five sacks, his lowest sack total since 2012.
The Cowboys have already lost a number of players to free agency, including defensive tackle Maliek Collins and defensive end Robert Quinn. Depth defensive linemen Christian Covington and Michael Bennett are also free agents.
McCoy, 32, is entering his 11th season.