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The Blues have reportedly paid £50m for the England international, who has put to paper on a five-year deal at Stamford Bridge.
Sterling, 27, leaves City having scored 131 goals in 337 games during a successful seven-year spell at the Etihad.
Sterling confirmed the move by posting a letter to City on Twitter, which read: "Seven seasons, eleven major trophies, a lifetime of memories.
"To the coaching staff who have played a massive role in my development over the years. To my teammates who have become more than just those | share a pitch with.
"To the backroom staff, to the office staff, to the fans who have tirelessly supported the team, and to everyone involved with Manchester City, my respect for you couldn't be greater. What a ride it's been.
"I am thankful for the ups and the downs, as it's the downs that have, at times, tested my strength and resolve, and enabled me to stand here in front of you as the best possible version of myself.
"I arrived in Manchester a 20-year-old. Today, I leave as a man. Thank you for your endless support. It's been an honour to wear the shirt of Manchester City."
City made Sterling the most expensive English player in history when they signed him in a £49m move from Premier League rivals Liverpool in 2015.
He would go on to play a major role in the club's success under Pep Guardiola, winning four Premier League titles, one FA Cup and the EFL Cup four times while in Manchester.
The former QPR youth player now returns to London and becomes Chelsea's first major signing in the post-Roman Abramovich era.
He is set to earn more than £300,000 per week at Stamford Bridge, making him one of the highest-paid players in the Premier League.
Chelsea confirmed the transfer on Wednesday evening, posting a picture of Sterling in the club's shirt on their tour of the United States, alongside with the caption: "A star in LA! #SterlingIs Chelsea".
"I've obviously achieved a lot in my career so far, but there is still so much more to achieve and I'm really looking forward to doing that in a Chelsea shirt, under Thomas's management,” Sterling told Chelsea’s website.
"London is my home and where it all started for me, and it's amazing I now have the opportunity to play in front of friends and family week in, week out at Stamford Bridge. I'm really looking forward to meeting the fans there soon.
"I do want to take the opportunity to thank Todd, Behdad, the ownership group, Thomas, and all involved in the process of getting me here. I can't wait to get going now and continue to do my talking on the pitch."
Chelsea's chairman and co-owner Todd Boehly added: "Raheem Sterling is a serial winner and his signing is an important step in strengthening our squad. We are delighted for Raheem to return to London with Chelsea, and we look forward to seeing his world-class talent on display at Stamford Bridge."
Featured Image Credit: Twitter & Chelsea
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