The 29-year-old moved to the Santiago Bernabeu on a season-long loan deal on transfer deadline day from Chelsea.
Essien made his La Liga debut last Monday and lasted the entire duration in the 2-0 win at Rayo Vallecano.
He is expected to play a key role in Sunday's clash against Deportivo La Coruna.
Essien seems to have settled in at the club and but admitted it has not been a smooth transition for him.
- The Spanish League is one of the most important and toughest Leagues in Europe, Essien told the club's official website.
- Many people speak of the Premier League as the best, but the Spanish League is more fun. You play more football and you score more goals.- The fans enjoy it. I am really looking forward to having a great season and to defending our title.