In an already competitive race to be the division's top scorer, Morata joined Sergio Aguero and Romelu Lukaku on six goals from as many games.
Costa had always been touted for a reunion with Simeone, with whom he won the La Liga title in 2014 and has made no secret of his desire to return to Spain, finding himself at the centre of various controversies such as being pictured partying in an Atlético shirt.
Asked if he had a message for the Chelsea fans, he said: "They know that I care a lot about them".
Alvaro Morata continued his stunning start to life at Chelsea with a hat-trick as the Premier League champions sealed an impressive 4-0 victory away to Stoke City. It turned into a matter of when, not if, Costa would return to Madrid.
"He is very happy", Fabregas said of Costa.
"I think we have to be focussed at what we do and not [on] others", said Conte. I hope this is also the best for Chelsea.
Costa returns as a hero at Atletico having led Los Rojiblancos to their only La Liga title in the past two decades and the Champions League final by scoring 36 goals in the 2013/14 season. Costa's back-door Chelsea exit is a bitter end for the striker whose goals landed two titles in three seasons for the south-west Londoners.
Conte had texted Costa to tell the Spaniard that he was not in his plans for the future at Chelsea, with Alvaro Morata signed from Real Madrid in the summer as his replacement.
Morata scored a hat trick in the 4-0 win at Stoke on Saturday and has netted six Premier League goals in all since his arrival. "This shows we trust him".
Hazard was part of a mix-and-match line-up featuring young players Kenedy and Charly Musonda, who both scored in a 5-1 win.
Diego Simeone's team moved one point behind leader Barcelona, which plays at Girona later.
However, even if club legend Fernando Torres leaves the club at the end of the season once his contract expires Atletico will still have plenty of options up front, and therefore Costa's arrival could trigger the exit for either Griezmann or Vietto.
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