The treble winners said the 29-year-old had signed a four-year contract after the clubs reportedly agreed an initial fee of £25 million, with a potential £5 million in add-ons.
Kovacic joins Pep Guardiola's side after five years at Chelsea, where he won the Champions League and Europa League and made 221 appearances.
He is City's first signing of the transfer window and his arrival compensates for the departure of Gundogan, who joined Barcelona on a free transfer on Monday after seven years at the club.
"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," said Kovacic.