The 56-year-old, who joined the Robins from Walsall in January, is based in the Midlands with his family and has found the travelling a strain.
"The club is in a position now where, if the right decisions are made, it can only go one way," O'Kelly told the club's official website.
"They are in good hands and I couldn't speak highly enough of the people I've worked with.
"I wish the club all the best in the future and I'm sure they will be successful."
O'Kelly worked under City head coach Sean O'Driscoll at Bournemouth and Doncaster - and the duo achieved promotion with both clubs.
Meanwhile, the club have also announced that sports scientist Kunle Odetoyinbo and goalkeeping coach Nigel Spink are also to leave the club this summer.