The 27-year-old announced his departure from City earlier on Wednesday and has now signed a five-year contract at Stamford Bridge.
Sources have told ESPN that Sterling joins Chelsea in a £47.5 million deal rising to £50m with add-ons.
- How will Sterling's arrival impact Chelsea's other forwards?
- O'Hanlon: Sterling's evolution into one of PL's best (E+)
- Stream ESPN FC Daily on ESPN+ (U.S. only)
- Don't have ESPN? Get instant access
It also means that City can recoup a transfer fee for Sterling, whose contract was set to expire next year, when the winger could have left the Etihad for free.
Sterling scored 131 goals in 339 appearances for City since signing from Liverpool for an initial £44m in 2015.
"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 Tuchel's] management," Sterling told the club'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 [Boehly], Behdad [Eghbali], 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."
The 27-year-old has helped City to four Premier League titles, an FA Cup title and four League Cup titles during his time at the Etihad, as well as a Champions League final defeat to Chelsea in 2021.
He became an integral part of Pep Guardiola's team after the Spaniard became City manager in 2016, but he has since fallen out of favour, starting just six of their final 11 league games as they won the Premier League last season.
Sterling has also become a key player for England during his time at City, scoring three times at last year's European Championship as Gareth Southgate's team reached their first major final since 1966.
Manchester United forward Cristiano Ronaldo has also been linked with a switch to Stamford Bridge. Ronaldo is open to a move to Chelsea, sources have told ESPN, after he signalled his desire to leave Old Trafford last week.