Raheem Sterling has scored 120 goals for Manchester City under Pep Guardiola - only Sergio Aguero (124) has managed more for the club since the manager's arrival in 2016
The 27-year-old has one year left on his contract at City and had attracted interest from major clubs overseas.
City signed Sterling from Liverpool in a £49m deal in 2015 and he went on to score 131 goals in 339 games.
Should the deal be completed, Sterling - who has 77 England caps - will become Chelsea's first major signing since they were taken over by a consortium led by Todd Boehly this summer.
It is expected the deal will be done in time for Sterling to link up with the Chelsea squad before they leave for their pre-season tour to the United States next week.
BBC Sport understands decisions all parties have been amicable but Sterling wants a fresh challenge and was impressed by Blues manager Thomas Tuchel's vision and the role outlined to him.
Other major clubs, including Barcelona, Real Madrid and Bayern Munich were also interested in Sterling but the player was swayed by Chelsea's public and privately stated desire to sign him.
City wanted Sterling to stay and he has no ill feeling towards the club or manager Pep Guardiola.
However, he views this as the most important contract of his career and wants to play a pivotal role at a club challenging for all the major honours.
Sterling still has team and professional targets he wants to fulfil, including winning the Ballon D'Or.
Apart from Manchester United players, only John Terry and former City team-mate Fernandinho have won more than his four Premier League titles.
However, he is still to win a Champions League.
Sterling instigated the conversation about his future with City and it is understood he appreciates the space he has been given to make his decision.
Tuchel was looking to boost his attacking ranks after Romelu Lukaku rejoined Inter Milan on a season-long loan.
The Belgium striker was the Blues' top scorer last season with 15 goals in all competitions, narrowly ahead of Kai Havertz (14) and Mason Mount (13).
Since Guardiola became manager in 2016, only Sergio Aguero (124) has scored more goals for City than Sterling (120).
Sterling scored 13 goals in 30 Premier League appearances last season as he won his fourth league title, his ninth major honour in seven seasons with City.
But his opportunities were restricted by last summer's signing of Jack Grealish, while forwards Erling Haaland and Julian Alvarez have arrived at Etihad Stadium this summer.
Sterling was on the bench for both legs of the Champions League semi-final defeat by Real Madrid and the epic final game of the season against Aston Villa.
However, he did spark that memorable last-day comeback by setting up Ilkay Gundogan's crucial first goal as City came back from 2-0 down to win 3-2 and pip Liverpool to the league title.
-- Courtesy of BBC Sport