Sportsmail understands the England forward has finalised a contract worth £315,000-a-week.
The clubs are still negotiating a fee — expected to be around £55million — but Chelsea go to the USA on Saturday for a pre-season tour and they want the deal done by then so Sterling can fly out with them.
Blues boss Thomas Tuchel has held talks with the 27-year-old concerning how he would be used at Stamford Bridge, which hardened Sterling’s desire to make the move.
Sterling, who is in the last year of his contract at City, will be the first marquee signing of Chelsea’s new ownership, spearheaded by chairman Todd Boehly.
Sterling’s desire to leave City was driven by a demand for more game time in the biggest fixtures, something City manager Pep Guardiola could not guarantee, but the relationship is ending amicably.
It is believed that City formally discussed Sterling’s desire to bring an end to a stellar seven-year stay at the Etihad Stadium at the beginning of the June during a conversation led by the England international.
The Premier League champions afforded the forward time to determine his next steps and Sterling has appreciated the space to assess his options and is thankful for the transparency that both parties have committed to.
Sterling will be remembered fondly by City supporters after lifting four Premier League titles under Pep Guardiola.
Last season he broke into the club’s top 10 list of all-time goalscorers, underling his influence during City’s spell of domestic dominance. He has openly credited the City coaching staff for his tactical development and views his time under Guardiola as hugely successful.
Driven by ambition he did, however, hope for more regular game time in the biggest fixtures – something Guardiola could not guarantee. Sterling played only 21 minutes of the two Champions League semi-final legs against Real Madrid, coming on as an extra-time substitute at the Bernabeu.
Sterling, who is now in the Premier League’s 100 goals club and won five domestic cup competitions at City, still harbours ambitions of lifting Europe’s biggest prize and achieving personal targets, understanding that this move will ultimately define his success as a player. Not content with making the shortlist for Ballon d’Or, Sterling has a strong desire to be in contention for the accolade.
Tuchel believes Sterling can offer more cutting edge to a Chelsea team who often failed to convert dominance last year and have allowed Romelu Lukaku to head back to Inter Milan on loan.
Only Riyad Mahrez and Kevin De Bruyne scored more goals than Sterling last season and it remains to be seen whether Guardiola looks for a replacement in attacking areas.
City expect big things of academy graduate Cole Palmer, whose season was hampered by persistent injury problems but who had impressed during cameo appearances.
Palmer’s likely promotion to a more prominent spot among the pecking order would see him alongside Erling Haaland, Julian Alvarez, Phil Foden, Jack Grealish and Mahrez as senior options in the attacking area