Chelsea visit Atleti in the Champions League on Wednesday, although Costa will not be eligible to play for the club until a FIFA-imposed ban on registering new players ends in January.
A Chelsea statement on Thursday said that they had agreed terms with the La Liga side for the transfer of Costa, with Spanish newspaper El Mundo saying the fee would be 55 million euros ($65.9 million).
The Premier League champions on Thursday confirmed they had agreed terms with Atletico for the sale of the Brazilian-born Spain global for a fee that could reportedly rise to €60million.
The Premier League champions last week agreed to sell the Brazil-born Spain worldwide back to Atleti for a fee that could reportedly rise to €60 million.
Costa joined the Blues from Atletico in July 2014, scoring 59 goals in 120 appearances.
Diego Costa insists he is not angry with Antonio Conte.
"Morata has got great potential, but I think Costa is someone that if you as an opposition manager you'd rather be facing Morata than Costa". "Now at this moment in time I think he is better suited to the English game", Neville told Sky Sports' The Debate.
"I'm proud of the club's efforts to bring a player who is among the top three strikers in the world", Atletico's Brazilian left back, Filipe Luis, said. "We want to fight in every competition we are playing". Last season he played No 9 twice, but I ask specific work to my strikers.
While Costa is a bulldozing centre forward never slow to go to war with central defenders, Morata goes about his business in a more refined manner, relying on stealthy movement and an ability to find space in the opposition penalty area.
"Diego knew that if he signed for Atletico he could not play for a few months". It is not easy to win away games against Stoke, this game is always hard.