The 27-year-old posted a goodbye message on social media ahead of an expected £50 million ($59 million) move.
Sterling announced his exit from the Etihad with a social media post thanking those he worked with at the club over the past seven years.
"Seven seasons, eleven major trophies, a lifetime of memories," he posted on Twitter. "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 as a 20-year-old. Today, I leave a man. Thank you for your endless support. It's been an honour to wear the shirt of Manchester City."
Sterling is set to become Chelsea's first signing since Todd Boehly's consortium bought the club.
What a journey ? pic.twitter.com/beX13AOOsj— Raheem Sterling (@sterling7) July 13, 2022
The England international won four Premier League titles among nine major trophies since joining City from Liverpool in 2015.
A key player in the early years of Pep Guardiola's reign at City, Sterling scored 131 goals in 337 appearances for the English champions.
However, his regular place in the starting line-up at City came increasingly under threat from the signing of Jack Grealish for a Premier League record £100 million last year, plus the emergence of Phil Foden from the club's academy.