The Brazil-born forward had long been linked with a move to the London side and completion of the deal appeared to be imminent after the Blues said earlier this month they had met the buy-out clause for the 25-year-old, whose transfer transfer fee could be in the region of £32 million ($55 million, 40 million euros).
“Chelsea Football Club is delighted to announce Diego Costa has today (Tuesday) completed his transfer from Atletico Madrid by signing a five-year contract,” a statement from the London club said.
“He will join up with the first team for our pre-season European training camp next week.”
Costa scored 35 goals for Atletico last season as they won the Spanish title and reached the Champions League final, only to lose in extra-time to city rivals Real Madrid after they had defeated Chelsea in the semi-final.
His desire to represent Spain, rather than Brazil, at this year’s World Cup in his homeland backfired spectacularly as the reigning champions crashed out in the first round.
Costa joins former Arsenal and Barcelona midfielder Cesc Fabregas in moving from Spain to Stamford Bridge this pre-season.
“I am very happy to sign for Chelsea,” Costa told his new club’s website. “Everybody knows it is a big club in a very competitive league, and I am very excited to get started in England with a fantastic coach and team-mates.
“Having played against Chelsea last season I know the high quality of the squad I am joining.
“I would like to thank everybody at Atletico who made me into the player I am, it was an incredible time for me, but now I am starting a new adventure and I hope to win many trophies with Chelsea.”
Despite his World Cup travails, Costa appears to have a big fan in Chelsea manager Jose Mourinho, with the Portuguese complaining that a lack of strikers — despite the presence of Fernando Torres, Demba Ba and Samuel Eto’o at Stamford Bridge — prevented the third-placed Blues from surpassing Premier League winners Manchester City and runners-up Liverpool last season.
Chelsea play RZ Pellets on July 23 before further pre-season matches in Slovenia, the Netherlands, Germany and Hungary.