The announcement came a day after Chelsea reportedly triggered a £10.5m release clause in the 27-year-old's contract, prompting him to withdraw from QPR's squad to face Sunderland.
"I feel very happy and very proud," said Remy, who was pictured on the Chelsea website posing with a club shirt. "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."
Remy has been signed to replace Fernando Torres, who has joined AC Milan from Chelsea on a two-year loan deal, and to provide competition for fellow strikers Diego Costa and Didier Drogba. Arsenal were also reported to have made a late move for the former Lyon and Marseille forward, but it was Chelsea who secured his signature.
"I remember the amazing atmosphere at Stamford Bridge when I played there for Marseille and I can't wait to play for the first time in front of my new fans," Remy added.
Remy would have moved to Liverpool in July, only to fail a medical for unspecified reasons, but Chelsea manager Jose Mourinho has played down concerns about his physical condition. Speaking before Remy had undergone a medical examination on Saturday, Mourinho said: "The information we have from specialists in different areas is he doesn't have a problem to play football."
Remy joined QPR in January last year, but following the club's relegation to the Championship, he spent last season on loan at Newcastle United, scoring 14 goals in 26 league games. The lithe, pacy striker, who can also play on the flanks, came through the youth system at Lyon and made his first-team debut in 2006.
After a spell on loan at Lens, he spent two years at Nice and then joined Marseille in 2010 despite a medical examination revealing a potential heart defect. His time at the Stade Velodrome saw him turn into a prolific centre-forward under the guidance of then-coach Didier Deschamps and in January 2013 he joined QPR for a club-record £8m fee.
He has played 25 times for France, scoring five goals, and made two substitute appearances at the FIFA World Cup™, where his country reached the quarter-finals.