The move is now subject to the player agreeing personal terms and passing a medical.
However, a deal has now been brokered between the clubs and Costa will join Atletico on 1 January.
Costa and Chelsea had a poor season in 2015/16, but then he was then back at his best to spearhead the club's charge towards more Premier League glory in 2016/17.
The Liga outfit announced on Thursday that they have agreed a deal with Chelsea to sign Costa for a fee thought to be in the region of £58 million.
Fare thee well, Diego, and thanks for the memories!
It means, therefore, that Atletico Madrid spent £23m to bring Costa back to the Spanish capital, bearing in mind what they received to sell him to Chelsea in 2014.
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At Island Empanada in Ronkonkoma, one of the Long Island's few Puerto Rican restaurants, diners were glued to television coverage. It was centered about 55 miles (90 kilometers) north of Punta Cana, Dominican Republic, and moving northwest near 9 mph (15 kph).
After his £32 million move in 2014, Costa was hugely influential in the two Premier League title wins Chelsea achieved in 2014/15 and 2016/17 respectively, and scored 59 goals in 120 appearances.
The Spain global is set to secure a return to Atletico after Chelsea agreed terms to the sell the striker who had been at the club since 2014. The club, the players and manager want Costa.
"Diego always said he wanted to come back, he always made that clear, and perhaps that made the situation a little more hard but it's normal, and we knew he wanted to come back". This is the first of three tough games in seven games.
Atletico can officially register Costa on January 1, when the Spanish transfer window re-opens and their Federation Internationale de Football Association transfer ban ends.
The Brazil worldwide said Costa, who had made it clear that he wanted to return to Atletico, has had "a complicated summer".
Chelsea signed fellow Spaniard Alvaro Morata in the summer transfer window, with Michy Batshuayi acting as his backup.
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