A source has told Goal that Atletico are hoping to stagger the payments by making the deal as an initial loan move from January with an obligation to buy in the summer transfer window.
A statement from Atletico Madrid reads: "Atlético 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."
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.
Antonio Conte and Costa fell out over the summer after the Chelsea manager sent a text message to remind the 28-year-old that he was no longer needed at the club while he was away with his national team. The deal will end months of disputes between the player and the club, with all parties thought to be relieved to have resolved the situation.
Costa's Chelsea career ends with him having won two Premier League titles and the League Cup after he moving in 2014 for £32 million to the Premier League.