The Ghanaian midfielder arrived at the Santiago Bernabeu on the last day of the transfer window, moving to the capital outfit from the Champions League title holders.
The agreement reunites Essien with former boss Jose Mourinho, with the pair formerly together at Stamford Bridge.
"Essien is a friend of Mourinho's," the Spaniard said at a press conference ahead of the Real's La Liga clash with Granada.
"(He) is a player who has the confidence of the coaching staff. He will be an important signing."
The Vitoria native went on to discuss the situations of peripheral names such as Kaka and Ricardo Carvalho, who remain on Madrid's books despite being linked with exits.
"(Mourinho) made it clear at different points in the summer. Most importantly, if Kaka was on the team, he would be one of the players we'd support," he added.
"Carvalho's case is different. Eventually we will see what decision is made, respecting the player's wishes and the circumstances."