"...the completion of the move is subject to him (Essien) agreeing personal terms with Milan and passing a medical examination," Chelsea said on their website.
Italian media reports said Essien was due to sign a contract that would keep him at Milan until June next year.
Essien joined Chelsea in 2005, during which time the west london club won the Champions League, the Premier League title twice and the FA Cup four times.
Earlier, Milan said on their website: "Just turned 31, and with a CV including domestic title and Champions League wins as well as victory with the Ghana national side, Michael Essien is expected in the city this evening".
- Sports & Recreation