The 26-year-old has signed a six-year contract at the Etihad Stadium and comes in as a replacement for Fernandinho, who departed the club this summer.
Phillips came through the Leeds United youth ranks and was instrumental in their promotion to the Premier League for the first time in 16 years in 2020.
He is City's fourth signing this summer after Erling Haaland, Stefan Ortega and Julian Alvarez.
Phillips made 235 appearances for Leeds after breaking into the first team.
Phillips said: "I am absolutely delighted to have joined Manchester City.
"City have again proved to be the best team in the country with an amazing squad and a manager in Pep Guardiola who is rightly considered to be the finest in the world.
"To be able to play under Pep and learn from him and his coaching staff as well as be part of such a fantastic squad is a prospect that I am incredibly excited about.
"City are a world-class club with world-class staff and facilities and it's a dream come true to have joined the club."
City director of football Txiki Begiristain added: "Kalvin is a player that we have long admired, and at both domestic and international level, he has proved his fantastic ability and quality over the past few seasons.
"His reading of the game, alongside his passing ability, energy and drive make him a formidable talent and he is a player who has a fantastic will to win.
"We feel he will be a superb addition to our squad and that he will complement our game perfectly.
"Everyone here is looking forward to watch Kalvin play and develop even further over the next few years."
Phillips' signing was confirmed on the same day Gabriel Jesus departed for Arsenal for £45m.
Phillips has won 23 caps for the England national team.
