The Dublin born midfielder was on loan at Stockport County earlier in the season midfielder and made 17 appearances for the League Two side. He has previously played for Cherry Orchard. He broke into the Wolves team and made a few starts towards the end of the season.
Gleeson has been brought in to compensate for the loss of defender Paul McShane following West Brom making it to the Championship play-off final. The youngster made his fourth senior appearance for Wolverhampton as a substitute in Wednesday night's meeting between the sides in the semi-final second leg.
Staunton wanted to call-up to striker Stephen Ward, but the former Bohemians star suffered an injury in the latter stages of Wednesday's game.