Having helped the Blues win their maiden title in Europe's premier competition, the Ghanaian is looking to win more silverware by teaming up with old boss Jose Mourinho
Los Blancos are aiming for an unprecedented 10th success at that level.
And the dynamic midfielder was positive about being reunited with Jose Mourinho, but admitted he was surprised to have moved to Madrid
He told Marca: "When I returned to Chelsea I never imagined that this could happen, but football is full of surprises."
Essien, who recently became the first Ghanaian player to feature in El Clasico said: "It's no secret that Jose Mourinho has had a huge influence on my career since I arrived in England.
"So when he showed an interest in bringing me to Madrid I did not hesitate at all. One minute I was preparing to play in the Super Cup in Monaco and the next I was packing to travel to Madrid.
He continued: "Mourinho expects his players to work hard, and he always demands the most of them. He aspires to win all competition, he is a winner and he will always be a winner."
Essien won the Champions League with Chelsea last season and he hopes to help Madrid record a 10th European trophy, he added: "It would be a great achievement for the club and for city, and it would also be great, at a personal level, to win two consecutive Champions Leagues."