Head coach Antonio Conte is poised to face questions on Costa at his pre-match media conference on Friday after the striker was granted his wish to return to Atletico.
The 28-year-old Brazil-born Spain international joined the Blues from Atletico in July 2014, scoring 59 goals in 120 appearances.
Costa won two Premier League titles in his three seasons at Stamford Bridge, but admitted to pandering for a return to Atletico as early as his first season in England.
And after months of acrimony, claim and counter claim, Costa has been granted his wish after the Blues and Atletico agreed a fee reported to be in the region of Â£58million.
Chelsea play at Atletico next Wednesday in Champions League Group C and all parties will be relieved the matter has been resolved.
Costa will now travel to Madrid from Brazil to finalise his move.
Atletico said: "Atletico de Madrid and Chelsea have reached an initial agreement for the transfer of Diego Costa.
"The agreement is pending the formalisation of the contract between our club and the Spanish international forward.
"The English club has authorised Diego Costa to travel to Madrid in the coming days to undergo medical tests and settle his contract with our club."
With Atletico under a transfer embargo and unable to register new players until January, Costa will have to wait to wear the red and white stripes again.
Costa last season submitted three transfer requests, one prior to the start of the campaign which ended with his second Premier League winners' medal, as his exit became fractious.
Relations with the Blues and Conte were damaged in January when Costa reportedly had his head turned by a big money offer from the Chinese Super League, which soon evaporated.
But Conte and Chelsea, together with the striker and his agent, Jorge Mendes, agreed Costa could leave that summer.
That version of events is disputed by Costa, who argued Conte was forcing him out after the Italian sent a text message saying the striker was surplus to requirements, despite having two years remaining on his contract.
Costa was granted an additional summer break, missing the pre-season tour to Asia, but then extended his exile as relations with Chelsea deteriorated further and lawyers became involved.
Pedro is expected to be fit to return from a leg injury at Stoke, but David Luiz will serve the second game of his three-match domestic suspension.
Conte is poised to tinker once again, after making nine changes for Wednesday night's 5-1 Carabao Cup win over Nottingham Forest.
Midfielder Tiemoue Bakayoko was involved in a minor car accident on his way home from training on Thursday
The France midfielder was not injured and is expected to be in the squad on Saturday at Stoke.
Source : PA