Atletico was banned from making transfers over the summer, which kept the move on hold.
He can not be registered as a player for the La Liga outfit until January, when the club's transfer window ban comes to an end.
Chelsea has annonced that Diego Costa is indeed heading towards Madrid and the Saga is nearly over.
But his end at Stamford Bridge came to an end when manager Antonio Conte sent him a text message over the summer telling him he was surplus to requirements.
He scored 58 goals in 120 appearances for the Blues, including 20 in the Premier League last season as Chelsea won the title.
Sky sources indicate Atletico will pay more than £50m for the Spain worldwide, who will now have a medical in Madrid and discuss personal terms.
The Spain worldwide has been linked with a number of clubs, but he has been adamant that he only wanted to go back to his old side.
The Brazilian-born Spanish worldwide did not return to west London this summer after being told via text message that Antonio Conte no longer had plans for the 28-year-old forward.
Costa at first refused to return to training at Cobham, opting to remain in his native Brazil.
Diego Costa leaves behind a very complicated legacy at Chelsea FC.
Atletico Madrid have agreed a deal worth £53m, according to Spanish newspaper AS, which would make Costa their record signing ahead of Radamel Falcao, who cost £33m from Porto in 2011.
A grudge match when the two sides meet in the Champions League next week will be avoided as Costa can't be registered until January.
He had previously helped Atletico to the La Liga crown and Champions League final before departing in 2014. Relations with Conte were damaged in January when the player reportedly had his head turned by a big-money offer from the Chinese Super League which soon evaporated.