Costa is unable to play for Diego Simeone's side until January, when their 18-month transfer embargo comes to an end.
Premier League medal in first season
The centre-forward, signed by Chelsea for £32 million in 2014, has spent much of the summer away from his employers, training alone in his homeland Brazil, after being told by Blues boss Antonio Conte that he is not in the club's plans for this season.
Costa had long 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.
The striker scored 20 goals last season as Chelsea won their second Premier League title in three years and has enjoyed a fruitful, medal-laden spell in London.
It wasn't all smooth sailing for Costa, however, with the striker struggling in front of the goal for the first part of the controversial 2015/16 season in which the then-reigning champions sacked manager José Mourinho, sitting in 16th-place at Christmas.
Guus Hiddink then took over as Chelsea interim manager for the second time and Costa rediscovered his goal scoring touch but it wasn't enough to lift the Blues above an eventual 10th-place finish.
Strained relationship with Conte
His relationship with current boss Conte appeared fractured from the start with the forward supposedly making clear to the incoming Italian that his heart belonged back at Atlético.
In January, it was revealed that the Spaniard had handed in a transfer request amid a big-money offer from Chinese club Tianjin Quanjian but the move fell through due to new rules regarding the Chinese Super League's policy on the acquisition of foreign players.
Costa will now complete look to complete a medical in the coming days in anticipation of his return to the Spanish capital in January.