"Everything went well, thank God," Morata told reporters as he left the Clinica Universidad de Navarra medical centre in Madrid, having flown to the Spanish capital from London on Saturday.
Morata, who passed through Atletico's youth academy before switching to local rivals Real Madrid, is to sign an 18-month loan deal Spanish media reports said, with an option to sign him permanently at the end of the season.
Morata, who also spent two years at Juventus, joined Chelsea from Real Madrid in 2017 for a reported 80 million euros ($91.30 million).
Despite a promising start to his career in the Premier League, with 10 goals in his first five months, Morata has had a disappointing year with the London club, starting fewer than half their league games under coach Maurizio Sarri.
"I'm very happy, I've spent days waiting for this," Morata added, also addressing his spell with Real, where he won one La Liga and two Champions League titles.
"I began my career at Atletico and the people who know where I come from and know my history know what this means for me. The past is the past, and it cannot be changed, and I'm very proud of it. I am looking forward to everything being completed so I can start training with my team mates."
Morata joins an Atletico side who are second in La Liga and in the last 16 of the Champions League but have struggled to find a suitable strike partner for talismanic forward Antoine Griezmann.
Croatian striker Nikola Kalinic has struggled for form since joining last year, making only two league starts and scoring twice.
Diego Costa, meanwhile, has had an unhappy return to Atletico since rejoining the club from Chelsea, scoring one league goal this season, and is currently recovering from foot surgery.
($1 = 0.8763 euros)
(Reporting by Richard Martin; Editing by Christian Radnedge)
