The Ghana midfielder joined the Londoners in 2005 during which time they won the Champions League, the Premier League twice and the FA Cup four times.
Essien spent last season on loan at Real Madrid. He made 256 appearances for Chelsea F.C., scoring 25 goals.
"To show Michael respect is to not stop him going," manager Jose Mourinho told the club's website (www.chelseafc.com).
"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," said Mourinho.