The 24-year-old Algeria defender has signed a contract until 2030 and is available for the group stage of the Club World Cup.
City begin their campaign in the newly-expanded tournament against Moroccan club Wydad AC on 18 June.
Algeria international Ait-Nouri joined Wolves in a £14.9m deal from Angers in 2021, having spent the previous season on loan, and made 41 appearances in all competitions last term as the club avoided relegation, scoring five goals and adding seven assists.
He is Wolves’ second high-profile departure of the summer, with Manchester United having agreed to sign Brazil striker Matheus Cunha for £62.5m.
City have already agreed a £46.3m deal to sign AC Milan’s Netherlands midfielder Tijjani Reijnders, adding to the £200m spent in the January transfer window.
Ait-Nouri said: “City are one of the biggest clubs in the world and the chance to play for the club is a dream come true.
“I am excited about working with and learning from Pep Guardiola and his coaching team and getting to train and play alongside such a world class group of players.”