The Croatia midfielder, 29, is set to join the Premier League champions for an initial fee of £25m, with £5m in potential add-ons.
Chelsea are continuing to sell players as they look to trim their large squad for new manager Mauricio Pochettino.
Fellow midfielder N’Golo Kante is also on his way out, having agreed to join Al-Ittihad in Saudi Arabia.
Kovacic joined Chelsea from Real Madrid 2019, initially on loan, before signing a five-year permanent contract.
The arrival of Kovacic will throw further doubt on Ilkay Gundogan’s Manchester City future, with the Germany midfielder’s contract about to expire.
Kovacic made 37 appearances in all competitions for Chelsea last season in a turbulent campaign which saw the Blues go through three managers before finishing 12th in the Premier League.
He was part of the Chelsea side who won the Champions League in 2021, coming on as a late substitute in the 1-0 final win over City.
At international level, Kovacic has made 95 appearances for Croatia, playing every game as they finished third at the 2022 World Cup.
(BBC Sport)