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.
Atletico said the 28-year-old Spain global, who left the club to join Chelsea in 2014, would have a medical in the next few days.
The move will see the Spain worldwide return to the club where he rose to prominence in the 2012-13 and 2013-14 campaigns, scoring 56 goals across the two seasons.
After informing Costa that he was no wanted at Stamford Bridge from Conte, Costa took action. He helped Atletico win the Spanish league and reach the Champions League final in 2014.
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"After three months without playing, but training a little, I'm not in as bad shape as people say", Costa, who has been accused of being overweight, insisted. "Each game is different and we can choose players who can make the difference".
"We wish him all the best for the future. I'm happy that my friend is back".
Atleti continues to have a ban from signing players. Atletico recently signed Spain forward Victor "Vitolo" Machin but he is on a loan with Las Palmas until January.
But Conte, whose side beat Qarabag 6-0 in their opening Group C match in the Champions League, expects Luiz to play at Atletico next Wednesday.
When asked in Sao Paulo if he was upset at the way Conte had treated him, Costa told Splash News: "There's nothing of the sort there, I'm not upset with anybody, I have no bitterness towards anyone".
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