Goal UK reported early last month that a deal worth 75m pound, including transfer fee and salary, was finalized at a meeting in London less than 24 hours after Costa's penalty helped Atletico Madrid to eliminate the Blues from the Champions League.
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Chelsea will pay around 43m euro for the striker, although a significant portion of the transfer fee includes agents' fees.
The move will also more than triple the wages of Costa, who is believed to earn around 50,000 pounds a week at the Vicente Calderon Stadium. Chelsea will hand the 25-year-old a five-year contract worth 150,000 pounds a week.
As reported by Goal in April, it had long been the plan of the west Londoners to confirm the deal before the World Cup, where he is expected to lead the line for Spain if he can recover from the hamstring injury that restricted him to just a short run out in Atletico’s recent Champions League final defeat to Real Madrid.
Representatives of the Londoners have held a series of meetings with Costa's camp in recent months and the set of talks around the two clubs' Champions League second-leg showdown closed the deal.
Costa emerged as Chelsea's top center forward target following an outstanding campaign for Atletico, which won La Liga as well as finished Champions League runner up.
The 25-year-old scored 36 times in 50 matches for his club in the recently completed domestic season and his 27-goal league haul was third only to Cristiano Ronaldo (31) and Lionel Messi (28).
Chelsea hoped to trigger the Brazil-born forward's release clause in January, when he was also being closely monitored by rival Arsenal, but the player did not want to leave mid-season.
Mourinho has made no attempt to hide his desire to recruit a blue chip center forward amid doubts over the futures of Torres, Eto'o and Ba. At least two of the trio are expected to leave in the summer, while Romelu Lukaku will hold talks with Chelsea chiefs this summer following a season-long loan at Everton.
Chelsea has been active in the transfer market following the completion of the domestic season.
The Londoners have agreed a deal with Paris Saint-Germain to sell David Luiz for an initial 49m euro although the French champion has yet to officially confirm the Brazilian’s arrival.
Mourinho is also looking for a new left back and a new central midfielder following the departures of Ashley Cole and Frank Lampard. Chelsea’s top midfield target is Juventus’ Paul Pogba and it is also monitoring the situation of Cesc Fabregas.