The Potters claim that the necessary paperwork needed to complete the deal was submitted to the FA and the Football League ahead of the transfer deadline time of 5pm on Monday evening.
However, because of the weather conditions the Republic of Ireland international full-back had been unable to travel to Stoke for a medical and to sign a contract that will see him join Tony Pulis's side on loan for the remainder of the season.
Because of the adverse weather conditions across Britain on Monday, the FA and Football League gave club's special dispensation on completing signings as long as they received emails or faxes claiming that the deal had been agreed in principal.
The departure of Kelly will come as a surprise to supporters as Blues have also allowed young full-back Jared Wilson to join Chesterfield on loan whilst Stuart Parnaby has also struggled with injuries in recent weeks.
Kelly is also more than capable of filling-in at centre-back and that is an area in which Blues had been expected to strengthen during the transfer window but a new signing in that department did not materialise.