The Kingston-born England forward has spent his summer holiday in Jamaica, but is now in LA to link up with his new teammates and complete his £50million move to the London club.
It will mark a return to the capital for the 27-year-old, 12 years after leaving Queens Park Rangers to join Liverpool when he was just 16 years old.
And he could make his Chelsea debut against London rivals Arsenal.
The Blues are in the United States for their pre-season tour and, while their clash against Mexican giants Club America may come too soon for Sterling to feature, he could be announced as a Chelsea player in time to face Charlotte FC on Thursday July 21 or the Gunners in Florida on Saturday July 23.
Sterling's future has been the subject of intense speculation this summer having entered the final year of his contract at Man City.
The winger has enjoyed a decorated career at the Etihad Stadium, winning nine major trophies - four Premier League titles, one FA Cup and four Carabao Cups - since joining Pep Guardiola's side from Liverpool in 2015.
But Sterling has not always seen eye-to-eye with the Spanish boss, and it is widely believed he was open to leaving City this summer to have a starring role at another club, having been a victim of Guardiola's heavy rotation throughout his City stay.
The 77-cap England international held talks with manager Thomas Tuchel over a move to Stamford Bridge earlier in the summer, and is said to be excited at the prospect of moving to Stamford Bridge.
Sterling would be the third major departure from City this summer after Fernandinho and Gabriel Jesus, who has joined Arsenal.
He will also become Chelsea's first major signing under new owner Todd Boehly.
While the Blues have been linked with sensational moves for Cristiano Ronaldo and Neymar this summer, former Chelsea defender Jason Cundy believes that a move for Sterling is more sensible.
Discussing potential signings, the talkSPORT host said: "I actually think that, I've said this many many times, I think Neymar is overrated. I'm not saying he's a bad player, I think he's overrated, that's my own take on that, I'm not so sure he'd fit in at Chelsea.
"Ronaldo, there's a part of me that's a little bit concerned that it's not going to be a Thomas Tuchel signing, it feels a little bit like a Todd Boehly one where he's come in with the money and he's getting seduced by one of the world's greatest ever players and he's available.
"And then there's Sterling, which for me makes so much sense, I don't quite know what he's going to cost but it feels and sounds like it's going to be a decent deal."