The Croatia international has signed a four-year deal with the European champions.
The champions have announced the 29-year-old has signed a four-year deal at the Etihad Stadium after the clubs agreed an initial fee of £25m last week, with potential add-ons of an extra £5m.
Kovačić joins Pep Guardiola’s team after five years at Chelsea, where he won the UEFA Champions League and the Europa League and played 221 games.
He is City’s first signing of the summer and his arrival offsets the departure of captain Ilkay Gundogan, who joined Barcelona on a free transfer on Monday after seven years at the club.
Kovacic said: “It’s a great move for me and I can’t wait to get started with City.
“Everyone who has watched this team under Pep knows how good they are. For me they are the best in the world.
“The trophies they have won are clear to everyone, but they are also the best side in football.
“Joining this team is really every footballer’s dream. I still have a lot to learn and develop and I know I can become a better player under Pep’s guidance, which is really exciting for me.
My plan now is to rest for a few weeks before returning to Manchester and preparing for the new season. I want to help this club stay at the top and win more trophies.”
Kovačič is a four-time winner of the Champions League, before joining the Blues he also won three times in Europe’s elite competition with Real Madrid.
The versatile player started his career at Dinamo Zagreb and also played at Inter Milan. He won 95 caps for his country and will inherit Gundogan’s number eight shirt.
City director of football Txiki Begiristain said: “Mateo is an excellent footballer.
“He can play as a ‘six’ or an ‘eight’, he has a lot of experience at top level clubs and he understands the Premier League.
“Bringing him to City was a very easy decision as he has the tactical and technical qualities we are looking for in a midfielder.
“He’s someone we’ve watched for a very long time and we’ve always been impressed whenever we’ve watched him. I’m glad he’s here.
“It’s a great signing for this club and I’m very excited to see what he can do with Pep and the rest of our backroom team.”