Nunes has agreed a five-year deal with Man City, the Premier League champions, and will wear the No 27 shirt.
“The opportunity to work under Pep Guardiola, one of the greatest managers ever, and alongside some of the best players in the world was something I couldn’t turn down," the 25-year-old told Man City's official website.
“I’ve learned so much during my season at Wolves and I’m excited to continue improving in the Premier League, a division which brings the best out of me.
“I’m really excited to get going, meet the fans and hopefully be a part of plenty more success at City.”
"It's a dream come true!" 💬— Manchester City (@ManCity) September 1, 2023
Matheus Nunes chats through making the move to City! 🌟
The Portugal international arrived at Wolves from Sporting last summer. While at the Lisbon club, he impressed Guardiola in the UEFA Champions League, the Spaniard calling him "one of the best players in the world" after City's 5-0 win in February 2022.
In his maiden Premier League campaign at Molineux, Nunes scored one goal and provided one assist. The goal against Chelsea won the Budweiser Goal of the Month for April 2023.
“He possesses real quality and will bring a fresh dynamic to this team," City's director of football Txiki Begiristain said. "He is a player who can play passes that open defences, he can beat players and he is technically excellent.
“Everyone knows Pep improves players – we have seen it so often – and we cannot wait to see how Matheus develops under his management.”
Nunes could make his City debut against Fulham on Saturday.
As part of a separate deal, Wolves signed City midfielder Tommy Doyle on a season-long loan.