Vick hadn't been involved in a full workout since he suffered a concussion in Sunday's 35-31 loss at Atlanta. Eagles officials said they were following NFL protocol regarding concussions.
But Vick took part in Thursday's practice and the Eagles said an independent neurologist had cleared the quarterback to play.
However, Reid hasn't stated Vick will be his starter Sunday, when the Eagles have their home opener against the New York Giants. He said this week he'd have all three of the quarterbacks on his roster ready to play Sunday.
Mike Kafka took over after Vick was injured Sunday and split first-team plays with Vick in walk-throughs earlier in the week. Vince Young is listed as the No. 2 quarterback but has been recovering from a hamstring injury.