The Portugal international completed his transfer to the Premier League champions on deadline day in a £53million move.
City saw an initial bid for the 25-year-old rejected last week with boss Pep Guardiola a long-term admirer.
In order to help force through a transfer, Nunes refused to train with his Wolves teammates.
He expressed his delight at sealing his desired move to City in his first words to the club as he prepares for life at the treble winners.
However, it seems his former side have been left less than impressed with how he acted to get the deal over the line.
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In a statement, Wolves sporting director Matt Hobbs said: "I was disappointed with how it ended, it wasn't necessary the stance Matheus took, but we ended with a good resolution for everyone.
"Matheus is a hugely talented player but would admit that last season he didn't hit the heights he expected.
"But it was a tough season for the team, so maybe he wasn't allowed to do that.
"We've lost a player with a lot of potential, a lot of ability, but the situation has led to us bringing a greater number of players in to improve the squad and provide competition in the group.
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"The players here want competition in training, so while we've lost a good player, it's made us a more competitive and better squad overall."
Nunes signed for Wolves from Sporting Lisbon last year and made 39 appearances during his only full season at Molineux.
His final game for the club came in their 4-1 Premier League defeat at home to Brighton a fortnight ago, in which he was sent off.
Nunes has now arrived at City as their fourth signing of the summer, following Mateo Kovacic, Josko Gvardiol and Jeremy Doku.
Guardiola's side have seen Tommy Doyle head to Wolves on a season-long loan, while they have bid farewell to Cole Palmer with the England youth international joining Chelsea.