The Spain international was unveiled at the Wanda Metropolitano on Saturday alongside Vitolo as Atleti’s transfer ban came to an end.
Costa won two Premier League titles and scored 58 goals in 120 games for the Blues before falling out with manager Antonio Conte, which prompted a return to Los Colchoneros, where he made his name before moving to England.
“I thank the club for the efforts to bring me back here,” the 29-year-old told reporters. “I’ve been waiting for this moment for months, I just want to return to form as soon as possible and get on the pitch to help the team.
“It’s true we are out of the Champions League but we’ll fight to reach the objectives we are still competing for. I learned a lot at Chelsea, it’s a great club and I only have good memories.”