After weeks of exile in Brazil, the striker finally agreed a move back to Simeone's team. Arriving in the Spanish capital on Friday, he was mobbed by reporters at Madrid airport where he admitted to having a 'special affection' for people at the club.
The 28-year-old lifted two league titles in his three seasons in London, but his stay ended in acrimony as he refused to report back to training when Conte told him he was no longer needed.
'I didn't want it to unfold as it did', Costa told 'Marca', not letting his exit sour his time at Stamford Bridge. 'I have a special affection for the people at Chelsea'.
'I don't want to have an ungrateful attitude towards Chelsea, because I was also very happy there and played in a great team'.
Diego Costa will be eager to get back to work with the team he served from 2010 until 2014, although Atletico's transfer embargo means he will not be able to play until January.
'Atletico Madrid is my home and here I am', he continued. 'I am very happy. [The negotiations] went on too long, but there was a happy ending in the end'.
'Now I'm waiting to see my team-mates and to train. I am not as unfit as some have been saying. There won't be a lack of determination on my part and I'll give my best, as has always been the case', said Costa.