The Redskins received written confirmation Thursday night from the neurologist.
Griffin suffered a concussion in a preseason game against the Detroit Lions on Aug. 20, although he later declined to say he had indeed suffered one.
"He's been practicing," Gruden said of Griffin, the 2012 NFL Offensive Rookie of the Year. "There is nothing he really hasn't been doing. He has been to all of the meetings. He has not missed anything because of this, just he's had to wait on the written clearance. That's all.
"I'm probably the only coach in the league that gets questions on their 46-man roster on a [Friday]. We have until Sunday afternoon to turn in our 46-man roster, and we're going to do that with everybody."
Griffin, who remained on the field throwing passes to an assistant coach more than an hour after Friday's practice had ended, was not made available for comment.
Two weeks ago, the team announced Griffin had been cleared, but the neurologist changed his opinion after further examining test results. A day later, the Redskins announced Griffin was not cleared.
Griffin, who also suffered a concussion as a rookie in 2012 and another while playing for Baylor University, did not play in the final two preseason games and lost his starting job to Kirk Cousins.