Kovacic has signed a four-year contract at the Etihad Stadium and becomes Pep Guardiola's first summer signing.
Man City have paid an initial £25m for the Croatia international, who still had a year left on his contract at Stamford Bridge.
Kovacic spent five years at Chelsea after initially joining on loan from Real Madrid in the summer of 2018 and made 221 appearances for the Blues, scoring six goals in total.
The former Inter Milan midfielder won the Europa League, UEFA Champions League, FIFA Club World Cup and UEFA Super Cup during his time at Chelsea.
Kovacic will reinforce Manchester City's midfield after they missed out on Jude Bellingham to Real Madrid and lost the services of Ilkay Gundogan to Barcelona.
Kovacic said: "This is a brilliant move for me, and I cannot wait to get started with City.
"Anyone 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 for all to see, but they are also the best footballing side out there.
"To be joining this squad really is a dream for any footballer. I still have plenty of learning and developing to do, and I know under Pep's management I can become a better player, which is really exciting for me.
"My plan now is to rest for a few weeks before coming back to Manchester to prepare for the new season. I want to help this club stay at the top and win more trophies."
Man City director of football Txiki Begiristain said: "Mateo is an excellent footballer.
"He can play as a six or an eight, has plenty of experience at top level clubs and he understands the Premier League. It was a very simple decision to bring him to City because he has the tactical and technical qualities we are looking for in a midfielder.
"He is someone we have monitored for a very long time and always we were impressed whenever we watched him.
"I am delighted he is here. This is a great signing for this club, and I am very excited to watch what he can do with Pep and the rest of our backroom team."
Kovacic has won 95 caps for the Croatia national team and has helped his country to podium finishes in the last two FIFA World Cups.
