Costa has had to be content with training for the last few months as the Rojiblancos served the final part of their FIFA ban.
With that sanction over once the clock ticks into the new year, Costa can finally get to work on the pitch.
"I've been waiting for this moment for a long time," he said to reporters at his unveiling.
"I just want to get in shape to play as soon as possible, I'm tired of training.
"You can tell I've already worked and prepared well to play, I'm here to help the team and score goals.
"Atleti are not in the Champions League now, but we are going to fight for what we have left."
Sat on the sidelines has clearly meant a lot of heartache for the striker.
"I need to play," he continued.
"As a bystander, I suffered more than as a player."
Asked what his time was like at Chelsea, Costa had his tongue firmly in his cheek.
"I learned English there," he laughed.
"Seriously, the supporters, the people at the club and my teammates helped me a lot.
"Chelsea is a great club and I only have good memories."