He can't play for Atletico now because the club is serving FIFA's ban from registering new players until 2018 for having broken rules regarding the transfer of underage players.
Despite netting 20 goals in the Blues' Premier League title-winning campaign a year ago, the Spain worldwide was informed by manager Antonio Conte during the summer - reportedly via text - that he was surplus to requirements this season.
Costa will have to wait before pulling on the red and white striped shirt of Atletico as the European transfer window is closed and Atletico are banned from registering new players until 2018 after breaching Federation Internationale de Football Association rules.
The deal is worth 60 million euros ($71.3m); Atletico will pay 55m euros with a further 10m euros in add-ons. That ensured he would not become cup-tied and therefore remains free to play in the competition for another team in the second part of the season. The transfer fee is rumoured to be around £58m in total, according to ESPN.More news: Toys R Us filed for bankruptcy and people are sad
Costa has not featured for Chelsea this season, after he was told through text message that he is not in Antonio Conte's plan.
Costa at first refused to return to training at Cobham, opting to remain in his native Brazil.
Atletico have also confirmed the agreement, stating that Costa will arrive for a medical and contract signing in the coming days.
He had previously helped Atletico to the La Liga crown and Champions League final before departing in 2014.