Atletico agreed a fee with Chelsea last week to re-sign Costa, who has now completed a medical and agreed personal terms to return to the Spanish capital three years after leaving for Stamford Bridge.
However, Atletico's six-month transfer ban means Costa will be unavailable to play for Diego Simeone's side until January and will have to watch Wednesday's meeting between the two clubs from the stands.
Antonio Conte has insisted that he holds no grudge against the 28-year-old, despite the pair falling out after the Chelsea manager texted Costa in the summer to remind his striker that he was no longer needed.
"Yes, as I said before, I have no problem with Diego Costa," Conte said when asked whether he will be happy to see Costa, who could be presented to Atletico fans at the game. "I said that we wish, for him, the best for the future. We want to thank him for the last season. But, I repeat, I have no problem with him.”
The deal will end months of dispute between the player and the club, with all parties thought to be relieved to have resolved the situation.
Atletico chose an initial loan move to spread the costs over two seasons and Costa will ultimately become their record signing.
Costa's Chelsea career ends with him having won two Premier League titles and the League Cup after he moved to the Premier League in 2014 for £32 million.