The defender completed his deal from Lokomotiv Moscow in January 2008, four months after the Special One left.
Ivanovic said: "I'm so happy because it is a pleasure to work with one of the best and most successful managers in the world. I know it's going to be hard but I'm happy and look forward to that.
"He is the best for what we can expect at Chelsea.
"Everyone who loves the club is so excited. A lot of fans will be so happy."