The 22-year-old agreed a six-year contract to join City as new manager Pep Guardiola continued a major overhaul of his squad in a bid to reclaim the Premier League title they last won in 2014.
“John is an excellent young English defender and we are all really pleased he is joining us," City director of football Txiki Begiristain told the club website.
"We have worked hard to bring him to City and we feel we are signing one of the best central defenders in Europe.”
Stones, who joined Everton from Barnsley in 2013 for three million pounds, is football's second costliest defender after Brazilian David Luiz, who moved from Chelsea to Paris St Germain for 50 million pounds in 2014.
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"I'm looking forward to the next stage in my career," Stones said.
"I've obviously seen what's going on here at the Etihad, it's an ambitious Club with a great manager so I can't wait to get stuck in and help achieve the goals."
Spaniard Guardiola, who joined the Manchester club from Bayern Munich at the end of last season, identified Stones as the perfect fit for his possession-based game.
“We want to help John show his quality with us and improve on what he has already achieved," Guardiola said.
"I like the way he plays the game and I'm looking forward to welcoming him into the squad."
Stones's name appeared in City's Champions League squad which was published on the UEFA website hours before the transfer was confirmed. The club admitted the mistake was a "huge embarrassment".
Stones became City's eighth signing of the transfer window after midfielders Ilkay Gundogan, Nolito, Aleksandar Zinchenko, Aaron Mooy and Marlos Moreno along with forwards Leroy Sane and Gabriel Jesus.
He could make his debut in City's opening Premier League game at home to Sunderland on Saturday.
(Reporting by Toby Davis and Ed Dove, Editing by Ed Osmond)
