Gregory missed all of last season for violating the league's substance-abuse policy.
The "fully cleared" status means Gregory can participate in practices and games, which wasn't the case under his conditional reinstatement. Rapoport was told the NFL liked the pass-rusher's plan and clinical resources in Dallas.
"I've never been more proud of any individual in my life," Gregory's attorney, Daniel Moskowitz, said in a statement last week. "I'm very excited for Randy and his daughter and the rest of his family."
Gregory has logged just one sack over 14 games during a career largely sideswiped by off-the-field troubles.