Costa scored 20 times in Chelsea's 2016-17 Premier League title-winning campaign, but the 28-year-old is said to have had a strained relationship with head coach Antonio Conte in the second half of the season.
The Spain international refused to return to Stamford Bridge for pre-season training after falling out with the Blues, and he has been strongly linked with a return to Atletico since the start of the summer transfer window.
A transfer ban meant that Atletico were unable to sign the 28-year-old during the recent window, but Costa, who can be registered to represent Atletico from January onwards, is now heading for Madrid to undergo a medical with the La Liga giants.
"Chelsea football club has today agreed terms with Atletico Madrid for the transfer of Diego Costa. The transfer will be subject to the agreement of personal terms and a medical," read a statement on Chelsea's official website.
It is understood that Chelsea have accepted an offer in the region of £53m, although this is still to be confirmed.
Costa's 27 league goals during the 2013-14 campaign helped Atletico land the La Liga title.