O'Kelly returned to be Saddlers boss Dean Smith's right-hand man in the summer having already left the Banks's Stadium last season for a brief stint in charge at Hereford.
But he has again departed the midlands outfit to be reunited with O'Driscoll, whom he worked alongside at Bournemouth and Doncaster.
The 56-year-old will be first-team coach at Ashton Gate on a rolling contract basis.
Chief executive Stefan Gamble said: "Despite our best efforts to keep him here, it was evident that the opportunity to work in the Championship and alongside Sean O'Driscoll was too good for Richard to turn down.
"Therefore, after lengthy discussions, it was felt that it was in the best interests of all concerned to allow Richard to take up this new challenge.
"We thank him most sincerely for his services to the club and wish him well in the future.
"The process of finding a successor has now begun and the compensation that we have received will be made available to the manager to fill the position and also strengthen the squad."