"The transfer will be a subject to the agreement of medical and personal terms".
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The negotiating process has been arduous after Atletico's transfer ban complicated the arrangements between the clubs and Costa still won't be able to play for his old club again until January.
Chelsea later confirmed that a deal had been done, although Costa will be unable to mark his return to the Spanish capital until January.
Costa was not included in Chelsea's 25-man squad for the Champions League group phase, ironically drawn in Group C along with Atletico.
Diego Costa celebrates scoring a goal for Chelsea.
Chelsea manager Antonio Conte expects David Luiz to play against Atletico Madrid in the UEFA Champions League, despite nursing a broken wrist. Chelsea has annonced that Diego Costa is indeed heading towards Madrid and the Saga is nearly over.
Costa has refused to return to Chelsea this season after accusing the Blues of treating him like a "criminal" and has been demanding they sell him to Atletico.
He returned to the first team, however, and ended the season with 20 Premier League goals as Chelsea lifted the title.
"I'm proud of the club's efforts to bring a player who is among the top three strikers in the world", Atletico's Brazilian left back, Filipe Luis, said.
As noted by Dominic Fifield of The Guardian, Atletico were keen to sign their former striker in the recent transfer window, although a deal wasn't done before the summer deadline.