Costa has refused to return to Chelsea this season after accusing the Blues of treating him like a "criminal" and has been demanding they sell him to Atletico.
"The English club has authorised Diego Costa to travel to Madrid in the coming days to undergo medical tests and settle his contract with our club".
In quotes reported by Marca, Costa told reporters at Barajas airport: "I'm very happy, It's taken a lot of time but it has a happy ending". I'm looking forward to giving my best as always, and hopefully things go well. "I'm pleased and I hope to see him tomorrow and to say hello to him".
In his time with the Blues, the Spanish global scored 59 goals in all competitions for the Londoners, and helped the club to two Premier League titles.
Costa has not played since last season's FA Cup final defeat to Arsenal, having spent the last two months in self-imposed exile in Brazil after being told by Blues boss Antonio Conte that he was not in his plans.
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Costa was deemed surplus to requirements by Conte in the summer, despite scoring 20 goals in 35 appearances last season as Chelsea cruised to the Premier League title.
Chelsea has announced the transfer of Diego Costa to Atletico Madrid for roughly $77 million after spending seasons with the Premier League side.
"There's nothing of the sort there, I'm not upset with anybody, I have no bitterness towards anyone at Chelsea". I'm not a person who is going to smear the image. Everyone knew that I wanted to return to Atletico Madrid, ' he said.
The Brazil worldwide said Costa, who had made it clear that he wanted to return to Atletico, has had "a complicated summer". "Atletico is my home and I'm here". I'm not afraid about stepping back onto the scales; but I am afraid of "Profe" Ortega's training sessions!
"I repeat - for sure we want to thank him for his effort last season, not only last season but in the period he played for Chelsea".
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