Chelsea boss Antonio Conte eased fears over David Luiz's wrist injury by insisting the defender will be fit for the trip to Atletico Madrid next week.
Diego Simeone's side are now banned from signing players after breaching Federation Internationale de Football Association rules regarding global transfers of players aged under 16.
It is understood that Chelsea have accepted an offer in the region of £53m, although this is still to be confirmed.
Costa spent four years at Atletico before joining Chelsea in July 2014 after they met his £32m buy-out clause.
At the time Costa seemed on the verge of signing a lucrative deal with Chinese Super League club Tianjin Quanjian.
However, Costa will not find himself straight back in action as Atletico have been officially banned from signing new players until January. It turned into a matter of when, not if, Costa would return to Madrid. Conte says: "I hope with this game to finish the speculation about him, about Chelsea, about me and him".
May 8: Costa scores his 20th goal of the Premier League season in a 3-0 win over Middlesbrough which takes the Blues within reach of the Premier League title.
The Spain global is due to undergo a medical on Thursday and will be officially unveiled as an Atlético player in the next few days.
Costa will join former Sevilla midfielder Vitolo in strengthening Atleti this winter as they look to make another assault on La Liga and the Champions League during their first season in the impressive Estadio Wanda Metropolitano.
Atletico face Chelsea in the Champions League next Wednesday. The Black Eagles were in talks with Chelsea over the summer for Costa and were keeping tabs on the star striker.