The Atletico Madrid striker has agreed personal terms and Chelsea have met the buy-out clause in the striker’s contract. The only delay has been because of the hamstring injury suffered by the Spain international at the end of the season.
But he is back in training with his country and yesterday passed a medical in Barcelona.
Chelsea boss Jose Mourinho has said he is looking for a striker that can ”open the gate” after missing out on the Premier League title last season in part because of a lack of goals.
Samuel Eto’o, Fernando Torres and Demba Ba scored just 19 in the league between them.
Costa, 25, scored 27 goals in 34 league starts for Atletico plus eight in the club’s run to the Champions League final.
Chelsea still face a fight to keep their player of the year Eden Hazard, though, despite giving him the No10 jersey he craved.
Hazard expressed his delight at being given the jersey this week and said that he is looking forward to the fans seeing him in it next season.
But Paris St Germain are set to tempt Chelsea with a bid, that could be as high as £60m, to sell them the Belgium midfielder.
Mourinho is also shaping up his side for next season as they look for replacements for Ashley Cole and Frank Lampard.
Chelsea are set to make a bid for Atletico’s Brazilian left-back Filipe Luis and their midfielder Tiago, who played under Mourinho at Stamford Bridge in 2004/5 and is available on a free transfer. Chelsea are also in the chase for Cesc Fabregas, who could be available for £30m from Barcelona.
The Spanish champions announced the signing of the goalkeeper Miguel Moya from Getafe yesterday, increasing the likelihood that Thibaut Courtois will return to Chelsea after three seasons on loan to battle with Petr Cech for the No1 jersey.