The Ghana international midfielder joined the Spanish club from Chelsea last summer on loan for the 2012-13 campaign.
"I couldn't turn down this opportunity and I enjoy every minute," he told reporters. "I want to work hard so that the team wins.
"At the moment everything's going very well. The months I've been here have been fantastic and I've loved my experiences so far. It's all been excellent and I hope to be able to continue this way.
"[Coach Jose Mourinho has] been magnificent to me. I'm really pleased to be here. He's smiling. He's always pleased, happy and working hard for the team. I've never seen him sad."
Essien has featured in 20 games in all competitions for Madrid so far this season.