The 31-year-old has found opportunities limited at Stamford Bridge since returning from a loan spell at Real Madrid last season and had permission from Jose Mourinho to leave.
A Chelsea statement on Friday night confirmed a deal had been struck with Milan for the Ghana international.
It read: "Chelsea Football Club and AC Milan have reached an agreement for the transfer of Michael Essien to the Serie A side.
"Essien has travelled to Italy and the completion of the move is subject to him agreeing personal terms with Milan and passing a medical examination."
Milan were one of a number of interested parties and earlier on Friday announced Essien was expected in northern Italy later in the day.
A statement on acmilan.com read: "Michael Essien in expected in the city this evening."
And after arriving in the Italian city, Essien told Milan Channel: "I'm happy to be here. I will do my best for Milan and I hope to be ready to play.
"I spoke with Mr (Clarence) Seedorf (the Milan head coach) two days ago. I cannot wait to be available.
"I really want to thank the chairman and the team and thanks to Mourinho, who has allowed me to wear the Rossoneri shirt.''
Essien made over 250 appearances for Chelsea after joining them from Lyon for £24.4million in 2005, although he also suffered from a number of serious knee injuries during his time in England.
This season he has only featured in 13 matches after returning from his loan stint with Madrid, where he also played under Mourinho.