Anelka joined Chelsea in a £15million move from Bolton and has signed a three-and-a-half-year deal with the Blues.
He told The Sun: “This is the team I wanted to join and I never want to go anywhere else again. I’m delighted everything has been sorted out.
“My time at Bolton was great and I want to thank everyone connected with the club for what they did for me. But this was too good an opportunity to turn down.
“I want to play Champions League football, I want to win trophies – and Chelsea can give me that.
“I’m really looking forward to working with Avram Grant and following his style of football because it suits my game. I’ve been really impressed by what he and the team have done this season in what were very difficult circumstances.
“They have had great results and are still challenging for all the trophies.
“The quality of players here is fantastic and the competition for places excites me.”