The 31-year-old Ghana international leaves Stamford Bridge after a trophy-laden stint which began when he was signed from Lyon in the summer of 2005.
He won the first of two Premier League titles in his first season at the club and was also a member of the Chelsea sides who won the UEFA Champions League, four FA Cups and a League Cup.
Jose Mourinho was the man who signed Essien for Chelsea and then took him to Real Madrid on a season-long loan deal in 2012, before the duo returned to London last summer.
Essien tweeted: "I have just signed my contract with one of the best clubs in the world. Im very happy and looking forward to winning with the team#ForzaMilan."
"I cannot wait to join the team in training and be a part of Milan's family,"
he added on Milan Channel.
"I am very happy to have spoken to (Milan boss) Clarence Seedorf, he is a nice person. It's a pleasure to have heard what Seedorf had to say about me.
"I always give my best and battle for the team from the first minute until the
last. I hope to achieve something important and give my best for Milan."
Essien made 256 appearances for Chelsea, scoring 25 goals, but his first-team appearances have been limited this season.
However, he captained the side in their 2-0 FA Cup third-round win at Derby earlier this month, which turned out to be his final start for the club.
Mourinho said: "To show Michael respect is to not stop him going.
"We would have been happy had he stayed, because he is a fantastic player for the team, but he's given everything for the club and a great chance arrived for his future.
"I know he can continue to play at a high level and I wish him success and happiness in Italy and at the World Cup in Brazil."
Cruciate injuries marred Essien's 2008/09 and 2011/12 seasons, and it had been speculated in the Italian media that he had failed his Milan medical.
However, the move has now gone through and Essien has reportedly agreed an 18-month deal.
The Chelsea website said: "Essien epitomised the 'team player', with his versatility marking him out as an integral member of the squad.
"Giving everything whenever he pulled on a Chelsea shirt, his ability to play at right-back or in the centre of defence, as well as his preferred midfield role, ensured his importance to a side competing up to the latter stages of multiple competitions.
"While scoring goals was not a very frequent occurrence, when they did come they were often spectacular.
"Everybody at Chelsea Football Club would like to thank Michael for his distinguished service and wish him the very best of luck for the next chapter in his career. He will always be welcome at Stamford Bridge."