The lineman was conditionally reinstated to the NFL in September but has yet to dress for a game. Instead, he has taken part in the acclimation period "to help facilitate his return to football before being able to practice and be eligible to play in games," per the NFL.
Gregory is eligible to return to the field Sunday against the Washington Football Team. He has not been active for a contest since Week 17 of the 2018 season.
The 27-year-old has been out of football following an indefinite suspension for violating the league's substance abuse policy in 2019.
The former second-round selection has drawn four suspensions since entering the league in 2015.
Gregory has tallied 11 tackles for loss and seven sacks through 28 games over three campaigns with the Cowboys.
The Nebraska product joins a Dallas defensive line featuring DeMarcus Lawrence, Tyrone Crawford, and Everson Griffin.