The transfer of the Brazil-born striker from the Champions League finalists and Liga leaders has apparently been agreed, with the deal set to be announced after Atletico face Real Madrid in the Champions League final on Saturday May 24 in Lisbon.
Costa, 25, is hoping to be fit for the final having missed Sunday's 1-1 draw with Malaga due to a hamstring strain, but the Spain forward is keen to try his luck in the Premier League with Jose Mourinho's side.
Chelsea have apparently triggered the buy-out clause in his contract in the hope of concluding a deal before any of their rivals in European football can get in on the act.
It has been reported that he will see sign a £150,000-a-week deal. But his arrival will not signal the end of Fernando Torres' spell at the club, with Mourinho telling Sky Sports he wants to keep the much-maligned Spain forward.
Costa has scored 36 goals this season, including 27 in La Liga, and was the subject of another protracted wrangle - between country of birth Brazil, and adopted homeland Spain, who he will represent at the World Cup after making his debut in the 1-0 win over Italy on March 5.
After failing to get picked up by any Brazilian teams as a youth, Costa played street football before moving to Europe aged 17, joining Portuguese side Braga.
He initially joined Atletico in 2007 but failed to make any first-team appearances, spending time on loan at Celta Vigo and Albacete before moving to Valladolid.
Los Rojiblancos exercised a buy-back clause after just one season and, following a loan spell at Rayo Vallecano, the 6'2" target man has gone on to score 54 goals for the club.
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