The deal is for £3m, which covers the initial fee the Potters paid for his replacement Dean Whitehead, a player who is expected to play a big part this season, whereas it was clear from Christmas onwards last season that Olofinjana Stoke career was on the slide.
The deal also means City have got back the £3m they paid for the Nigerian international when signing him from Wolves last summer.
French side Monaco had agreed a £2.5m fee with Stoke for Oli, the player passed a medical and agreed terms before a last minute bid from Hull give the midfielder the chance to choose between Monte Carlo and Humberside. Humberside won the battle as it allows the African to continue to ply his trade in the Premier League, something he expressed a desire to do earlier this summer, and also continue his studies for a second degree, he is partway through a course at Aberdeen University.