Jose Mourinho's side had been seeking a replacement for Fernando Torres, who joined AC Milan on a two-year loan on Friday.
Remy, who spent last season on loan at Newcastle, has signed a four-year deal with the club.
Arsenal had also been linked with the 27-year-old.
"I feel very happy and very proud," Remy said today. "When I heard Chelsea wanted to sign me I said "let's go" straight away because they are one of the best clubs in the world."
His former manager at Rangers, Harry Redknapp, admitted yesterday that he is disappointed to lose the Frenchman but doesn't blame him.
"I didn't see it coming at all," Redknapp told Sky Sports News HQ. "Maybe I'm a bit naive but I was hoping he would be with us, he's a good player and he's important to us.
"He didn't refuse to play today, I just felt when people rang me up at 12 o'clock - I didn't know anything before 12 - I needed 11 people whose mind was on getting points for QPR and to be fair to him his head is not going to be right today."