Gregory, who has missed 30 of the past 32 regular-season games for multiple violations of the league's substance abuse policy, was conditionally reinstated last week pending details on his clinical resources in Dallas and confirmation that he is abiding by the league's substance abuse policy.
The Cowboys will have to make a roster move because they are already at the 90-player limit. Players report for training camp on Wednesday.
"My story is so much more than just what it looks like on the surface, where people thinking I'm a weed smoker and sitting around, just a pothead," Gregory told ESPN last week. "That's probably a fifth of what we've done the last two, three years. To say I've come back from all of that and on the right track mentally and physically, it's a blessing."
Gregory went through rehabilitation, held a job and put his life in order during his time away from the Cowboys. He met with NFL commissioner Roger Goodell last month in New York as part of the reinstatement process, and his legal team, led by attorney Daniel Moskowitz, supplied the league a vast array of test results, recommendations and personal letters from teammates Sean Lee, Tyrone Crawford and Jeff Heath.
Gregory fell to the Cowboys in the second round of the 2015 draft because of off-field issues during his time at Nebraska. Jerry Jones was willing to take a chance on Gregory and hoped that a support system that helped other players through the years would help Gregory.
Gregory played in 12 games as a rookie in 2015, missing four with an ankle injury. He ended up in the NFL's substance abuse program in 2016 and was initially suspended the first four games of that season. Another failed test led to an additional 10 games, but he was able to return for the final two regular-season games and recorded the first -- and so far only -- sack of his career.
He was suspended for a year before the 2016 playoffs and has not been around the team since.