The 21-year-old has already accepted a move to Stamford Bridge. Personal terms are expected to be a formality and a medical is now being scheduled.
The Blues had a £35m bid rejected earlier on Wednesday but rapidly returned to the negotiation table to agree a deal for the forward, who was on the fringes of Pep Guardiola’s squad.
Former City scout Joe Shields, who is now co-director of recruitment and talent, was key to securing the deal.
Palmer has struggled to establish himself at the Etihad Stadium and was an unused substitute in the treble winners's last two games despite scoring in the Super Cup win earlier in August.
He is still highly regarded having played a crucial role in England Under-21s European Championship win this summer.
The move will tip Chelsea’s summer spending beyond the £400million mark, and beyond £1billion for the three transfer windows since the Boehly-Clearlake takeover.
The arrival of Palmer will be Chelsea final spending of the window, with player sales set to top the agenda until Friday’s 11pm deadline.
Romelu Lukaku’s loan move to Roma is expected to go through imminently, while talks remain ongoing for Callum Hudson-Odoi’s permanent move to Nottingham Forest.
Ian Maatsen, Conor Gallagher and Trevoh Chalobah all continue to have uncertain futures. Maatsen has interest over a permanent deal from both West Ham and Burnley, while Chalobah is a target for Bayern Munich.
Tottenham continue to track Gallagher’s availability having been offered the chance to sign him previously.