British media are reporting that the deal could be worth around £50million, with the teams coming to an agreement over a deal after weeks of negotiations.
On returning to London to play for the Blues, Sterling told the official Chelsea website: "First and foremost, it’s a pleasure to be here.
"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."
He is right to say he has achieved a lot. Sterling has won four Premier League crowns since moving from Merseyside to Manchester in 2015. He has also racked up plenty of goals, hitting double digits in each of his seven campaigns with the Citizens.
Now, he returns to London, where he started his youth career with Queen's Park Rangers, something he is looking forward to.
He added: "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 can’t wait to get going now and continue to do my talking on the pitch."
He also had a parting message for City fans: "What a ride it has been. I arrived in Manchester as a 20-year-old, today I leave as a man.
"Thank you for the endless support. It has been an honour to wear the shirt of Manchester City."
Questions will now be raised about how the England international, who played an integral part in getting the Three Lions to the Euro 2020 final last year, will fit into Tuchel's plans, with a squad already stocked with attacking talent.
Reports are already surfacing about frustrations amonst the Chelsea team, with players like Callum Hudson-Odoi, Christian Pulisic and Hakim Ziyech all to have less game time with the arrival of Sterling.
Right now, the winger has joined up with his teammates in Los Angeles as they get ready to take on Club America on Sunday with Sterling likely to get some minutes.
Todd Boehly, newly-appointed chairman and co-controlling owner, added: "Raheem Sterling is a serial winner and his signing is an important step in strengthening our squad."
