As reported by Sky Sports, the Spanish international completed his medical with the Blues, clearing the way for a £32 million transfer move:
Chelsea have met the buy-out clause in the 25-year-old's contract with Atletico and he will now negotiate personal terms.
Costa was one of the revelations of the 2013/14 season, scoring 36 goals in 52 games for Atletico as they won the La Liga title for the first time since 1996.
He had to limp out of Atletico's Champions League final defeat to city rivals Real last month after just nine minutes but is now training with the Spain squad ahead of the World Cup in Brazil.
Blues boss Jose Mourinho made a striker his summer priority after Fernando Torres, Samuel Eto'o and Demba Ba all struggled for goals last season.
Costa was one of the driving forces behind Atletico's phenomenal 2013-14 campaign that saw them win La Liga and make it all the way to the UEFA Champions League final.
The Brazilian-turned-Spaniard had long been linked with a move to West London, as Jose Mourinho emphasised his plans to look for new attacking options all season long.
Costa's talent is obvious, and there's no denying his success in 2013-14. Per WhoScored.com, the forward scored 35 goals in 44 matches across La Liga and the Champions League, one of the highest marks in Europe.
He struggled with injuries late in the season, including an odd cameo in the Champions League final that lasted for just nine minutes, leading to a number of hilarious tweets from fans:
How the injury will affect his performances during the upcoming World Cup is anyone's guess, and the fact that the player reportedly passed a medical while being doubtful for such a tournament is curious at best.
Costa's current injury is a reason for concern for the Blues, but it's not the only reason why Mourinho is taking a big risk.
Atletico have a reputation for developing world-class strikers, having moved Fernando Torres and Radamel Falcao for massive transfer fees in recent years. Faclao was the team's go-to-guy last season, and when the Colombian left, Costa stepped right into his role and performed.
His production the year before? A total of 12 goals in 36 matches, per WhoScored. Not bad, but not nearly as impressive as his 2013-14 season.
Players have breakout seasons all the time, and it's entirely possible Costa finally lived up to his potential in 2013-14. But for a move worth £32 million, one season is a very small sample size.
Costa is a big forward with surprising technical ability for a man his size. He has great vision with the ball at his feet and times his runs away from the ball beautifully.
But Costa is used to playing with space, something that is often hard to come by in the Premier League. For a man his size, he isn't particularly physical. He doesn't use his natural abilities to win battles in the air the way you'd expect a top striker to, and he's not great at shielding the ball either.
Costa might look like Chelsea legend Didier Drogba, but he doesn't play the game the same way. He's not a classic target man—instead, he's an excellent presence in and around the box, and he seemingly scored with his eyes closed last season.
The Spaniard got a taste of the English game against Chelsea in the semi-final of the Champions League last season, scoring from the spot in the return fixture. The Blues neutralised his threat quite easily in the first match, playing him very short and dominating Costa in the air whenever a cross came in.
You'd hope defenders would never try to intentionally hurt a player, but Costa's injury history and the fact that he looked uncomfortable with Chelsea's close marking will make him a prime target for defenders in the Premier League next season.
Teams will test him early and often, and how he'll deal with such a step up in physicality will go a long way in determining the success of this transfer move.
Finally, there's one more catch: Romelu Lukaku enjoyed a very strong season on loan with Everton and has lit it up with the Belgian national team in the last few weeks.
People who claim Lukaku should be sold because "he didn't look great in pre-season" are overlooking the fact that he's still just a 21-year-old whose production has improved with every passing season.
Transfer Sources believe the youngster could be part of a deal for Costa, while John Cross of The Daily Mirror reports that Valencia are looking into buying the player:
Selling Lukaku would be a mistake. The Belgian has long been touted as one of the world's best up-and-coming strikers and has done nothing to suggest otherwise during his time at the club.
As for sending him on loan once again, fans have seen what too many years away from a club can do to a young player. Thibaut Courtois has developed into a world-class stopper with Atletico but has repeatedly made it clear he has become fed up with his current situation, with this comment taking the cake, via Nigeria Newsdesk:
Chelsea don't want to repeat this situation with the insanely talented Lukaku, and bringing in a veteran striker isn't going to help the relationship between Lukaku and the club one bit.
Costa has injury concerns and only one year of truly great production. He's not as physical as you'd like at his size and could stand in the way of Lukaku's future at the club.
The Spaniard has every chance of being a rousing success at the club, but it is far from a guarantee. Fans better hope the player is a slam dunk from day one, because this move could backfire in more ways than one.