— Chelsea FC (@chelseafc) August 31, 2014
The Frenchman has signed a four-year contract, that will keep him at the Stamford Bridge until the summer of 2018.
The Blues triggered a £10.5million release clause for the 27-year-old striker, who had also been linked with Premier League rivals Arsenal.
The Former Marseille man joined Rangers in January 2013, scoring six goals in 14 games. Since then, he spent the remaining 2013/14 campaign on loan at Newcastle United, where he scored 14 goals in 26 Premier League starts.
Remy is seen as the replacement for Fernando Torres, who joined Italian side AC Milan on a two-year loan deal.