Essien seals move to AC Milan
The 31-year-old midfielder joined the Blues from Lyon in 2005 and made 256 appearances for the club, also enjoying a season on loan with Real Madrid in 2012-13.
His first-team opportunities at Stamford Bridge had been limited in the current campaign and he has therefore now opted to pursue a career in Serie A.
Milan published a photograph of Essien posing with Milan vice-president Adriano Galliani on their official Twitter account, while Chelsea announced the deal on their official website.
Manager Jose Mourinho told his club's website: "To show Michael respect is to not stop him going.
"We would have been happy had he stayed because he is 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."
Essien was in Milan to undergo a medical on Monday and put pen to paper on a contract that will see him remain with the Rossoneri until June 2015.
A statement from AC Milan read: "AC Milan announce they have acquired Michael Essien from Chelsea. He has signed a contract until June 30, 2015."
Essien becomes Milan's third reinforcement in the winter transfer window following the arrival of Japanese playmaker Keisuke Honda from CSKA Moscow and French defender Adil Rami from Valencia.
The experienced midfielder joins a side that have struggled to make an impact this season and sit ninth in the Serie A table, 28 points behind league leaders Juventus.
Milan sacked coach Massimiliano Allegri earlier this month and appointed former midfielder Clarence Seedorf as his replacement.
The Rossoneri, who were eliminated from the Coppa Italia last week, are still alive in the Champions League and will take on Atletico Madrid in the last 16 of the competition next month.
Essien could make his Serie A debut in Sunday's match against Torino at San Siro.