Gregory's lawyer, Daniel Moskowitz, also confirmed to NFL Network's Ian Rapoport that Gregory's petition for reinstatement "was not opposed."
Rapoport reported in May that Gregory had formally filed his application for reinstatement, adding the 2015 second-round pick had returned from a six-week program that included "intensive drug and alcohol rehab in addition to counseling."
Gregory reacted to the news on Tuesday:
Gregory hasn't played a snap since the final week of the 2016 regular season. He appeared in two games that year after serving a pair of suspensions totaling 14 games.
The NFL suspended Gregory a third time in January 2017, this time for a minimum of one year.
His off-field concerns go back to when the Cowboys selected him in 2015.
Bleacher Report's Matt Miller ranked the former Nebraska star as the ninth-best player in that year's draft class, but he slipped to Dallas with the 60th pick. His stock fell following a positive test for marijuana at the NFL Scouting Combine.
Cowboys owner Jerry Jones threw his support behind Gregory as he sought reinstatement.
"He's really a good person. That goes a long way," Jones said, per ESPN.com's Todd Archer. "He's smart. That's redeeming. In other words is there a chance that he could get this figured out and be accountable and responsible? There is. Oh, there's one other little thing: He's one helluva football player, OK?"
There's no question Gregory has a role for the Cowboys in 2018. Dallas was tied for 15th in sacks (38) and 14th in adjusted sack rate, per Football Outsiders, and the team did little to improve the defensive line.
The Cowboys placed the franchise tag on Demarcus Lawrence and signed Kony Ealy, who has had a somewhat disappointing NFL career after the Carolina Panthers selected him in the second round in 2014. They also selected Kansas defensive end Dorance Armstrong in the fourth round of the 2018 draft.
Gregory could be a situational pass-rusher in 2018 before assuming a larger role in 2019 if Dallas can't work out a long-term extension with Lawrence.