Pep Guardiola's side have had a long-standing interest in Ait-Nouri and have now moved for the 24-year-old, who has departed after five years at Wolves.
A £33.7million deal was agreed over the weekend, with around £2.5million in add-ons, and the move has now been announced after Ait-Nouri completed his medical.
The Express & Star understands that the add-ons are related to Ait-Nouri's appearances and City's success in the coming years.
Before the deal with City was agreed, Wolves also bought out the 50 per cent sell on clause in place from former club Angers for around £9.5million.