The Spain international departs Stamford Bridge having won two Premier League titles and one EFL Cup, returning to the club from which he arrived three years ago.
In that time, Costa made 120 appearances for the Blues and scored 59 goals, finishing as the club's top scorer in each of his seasons on Chelsea's books.
The 28-year-old was involved in a stand-off with the club this summer after Antonio Conte reportedly texted his player to inform him that he was surplus to requirements.
In response, Costa refused to return to Stamford Bridge, remaining in his native Brazil, accused the Blues of treating him like a criminal and made it clear that he only wanted to join his former club.
A deal could not be reached in the summer window, but last week the clubs confirmed that an agreement has been made to complete a transfer in January for a reported £53m fee.
Even if Costa had joined Atletico in the summer, he would have been ineligible to play until 2018 due to a transfer embargo imposed on the Spanish club, which prevents them from registering new players.