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.