The deal, which will reportedly cost the Potters £500,000, was in doubt after Kelly failed to put pen to paper before Monday's 5pm deadline. However, the Premier League had said that they would allow deals to take place where it could be proven that both clubs and the player concerned had agreed to the deal, but that the adverse weather conditions had made the deadline unreachable.
Ireland full-back Kelly had been a regular for Birmingham since his move from Spurs until an injury this season left him out of the team and unable to reagin his first team spot.