Financial details were not disclosed, but British media reported City paid a fee of around 33.7 million pounds to sign the 24-year-old, who had one year left on his Wolves contract.
Ait Nouri initially joined Wolves on loan from Ligue 1 side Angers in 2020, before making the move permanent the following year. He leaves Wolves after five seasons, having made 157 appearances with 12 goals and 19 assists.
Speaking to the club website, Ait Nouri said: "I am incredibly happy and honoured to have joined Manchester City.
“I am also excited about working with and learning from Pep and his coaching team and getting to train and play alongside such a world-class group of players."
Director of Football Hugo Viana added: "Rayan is a player that, as a club, we have been following closely for quite some time and we are delighted he has joined us,” he began.
“He already has extensive Premier League experience and has also demonstrated his quality at international level with Algeria."
Wolves are now without two of their key players from last season, after Brazil forward Matheus Cunha's transfer to Manchester United on June 1st.
City finished third in the 2024-25 Premier League season and only secured a Champions League berth on the final day of the campaign.
Pep Guardiola's side are next in action at the Club World Cup in the United States. They face Wydad AC in their opening game on June 18th, before taking on Al-Ain and Juventus in their other Group G fixtures.
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