The Liga side confirmed on Tuesday that they had wrapped up a deal to bring the Spain international back for a second spell.
"Some cycles begin while others end. My cycle at Chelsea began three years ago - three remarkable years in all aspects - and I will never forget it.
"Two championship titles, a Community Shield, 120 matches, 59 goals and 24 assists later this cycle has ended. Not the way I would have wanted—far from it—but the best way possible.
"The wonderful fans of such equally admirable club and all team-mates, as well as all clinical, administrative and logistics staff will remain forever in my mind and in my heart.
"Will bring them with me with the certainty that I will always be by their side as well, and I'm sure they will understand the reason why this cycle of mine has now ended - because I could not lose faith in myself. Thank you Chelsea for everything!"
While mentioning team-mates, the message didn't include any note of Chelsea manager Antonio Conte or his coaching staff.
As Costa noted, his exit from Chelsea hasn't been on the best terms, with reports suggesting Conte sent the striker a text message to advise him he wouldn't be part of the squad for the upcoming season.
The striker joined Chelsea from Atletico in 2014 and became a huge fan favourite at Stamford Bridge.
Costa is the type of striker that's adored when he plays for your team and despised by opponents. His abrasive and aggressive style of football was perfectly suited for Premier League matches, while his short temper often prompted skirmishes on the field. When he was in the XI, you could guarantee entertainment.
Dean Jones summed up what English football will be missing now the transfer back to Atletico is done:
His personality meant his footballing skills were sometimes overlooked, though. Costa was not only a pest to opponents, he'd regularly get the better of his rivals in duels through a sheer determination and unashamed will to win.
Plus, he was a prolific goalscorer. Whether the ball was on his right foot, left foot or crossed to his head, Costa was a clinical taker of chances and often the man who'd grab a decisive goal for the Blues.
Here's an example of how ruthless and successful the 28-year-old was during his time with the club:
Chelsea and Conte will be keen to move on now, with the issue of the forward's future lingering over the club all summer.
When asked whether he would shake hands with Costa when Chelsea face Atletico in Madrid on Wednesday, the Italian denied there was any animosity lingering, per Mark Ogden of ESPN:
Costa will not be able to play for Atletico again until January due to the club's transfer ban and the fact a deal wasn't done in the summer window.
Ultimately, all parties involved in this transfer saga will be pleased it is at an end. Atletico are bringing a heroic figure back to the club, Costa has the move he wanted, while Chelsea have received a big fee for an unhappy forward, and in Alvaro Morata, they appear to have secured an excellent replacement.