The France international striker has put pen to paper on a deal until the summer of 2018, after Chelsea activated a £10.5million release clause in the 27-year-old's contract.
Remy joined QPR from Marseille in January 2013, scoring six goals in 14 games, as Rangers were relegated from the Premier League.
He then spent the 2013/14 campaign on loan at Newcastle United, where he scored 14 goals.
Remy, who had also been linked with Arsenal, told Chelsea's official website: "I feel very happy and very proud.
"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.
"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 came through French side Lyon's youth academy and made his first-team debut for his home-town club in 2006, playing for them during two Ligue 1 title-winning seasons, as well as in the Champions League.
However, it was at Nice, following a loan spell at Lens, where the young Remy built his reputation, earning a move to Marseille in August 2010.
He scored his first Champions League goals during his opening season for Marseille, playing in two group games against Chelsea, and was their top league scorer with 15 goals in 2010/11.
He made his international debut in June 2009, scoring his first international goal the following season.
After averaging almost a goal every two games during two and a half years at Marseille, in January 2013 he moved to QPR and scored on his debut at West Ham.
After Rangers were relegated, he joined Newcastle on loan last season, with his goal against Chelsea at St James’ Park in November one of 14 he scored in the Premier League last season.
He also travelled with the France squad to the World Cup in Brazil in the summer, making two substitute appearances.
He played in QPR's first two league games this season but not in their Capital One Cup defeat by Burton Albion, so remains eligible to play for Chelsea in all competitions.
Remy had looked set to join Liverpool earlier this summer but the proposed switch to Anfield broke down following a medical.
However, Chelsea boss Jose Mourinho said on Saturday: "The information we have from specialists in different areas is he doesn't have a problem to play football."
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@tremor - please remind me again how many matches Ba and Remy have missed due to injuries in the past couple of years? very few mate- isildur1