The striker passed a medical earlier in the week and has now all but confirmed his impending switch from the Liga champions after making his return for Spain on Saturday
It was revealed recently that he has already passed a medical with the Stamford Bridge club after a deal worth €43 million was finalised at a meeting in London.
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"Am I going to Chelsea? It looks like it," he told reporters.
The move is expected to more than triple the wages of Costa, who is believed to earn around €61,000 a week at the Vicente Calderon Stadium. Chelsea will hand the 25-year-old a five-year contract worth €185,000 a week.
Mourinho has made no attempt to hide his desire to recruit a blue chip centre-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 has now asked to leave the club in light of Costa's impending arrival as he searches for regular first-team football.