Both clubs have agreed a fee around £53million for the 28-year-old, who would not be eligible to feature for the La Liga side until January next year.
Costa has not played for Chelsea this season too, as he tried to force a move back to Spain.
He told Splash News when pressed on whether he was upset by Conte’s treatment of him in west London: “There’s nothing of the sort there, I’m not upset with anybody, I have no bitterness towards anyone. Everything is cool.”
Costa was speaking at an airport in Sao Paulo as he finally prepares to return to Europe.
Asked if he had a message for the supporters he is leaving behind at Stamford Bridge, Costa said: “Everybody knows how much I love the fans.”