The Primera Division champions announced last month they had agreed a deal to sign the highly-rated 19-year-old forward on a five-year contract, subject to a medical.
That medical revealed a cardiac condition and, on the advice of specialists, the Argentinian forward - who has been compared to compatriot and former Atletico hero Sergio Aguero - has decided to have an operation.
An Atletico statement read: "Angel Correa will undergo microsurgery in the coming days to resolve a heart condition that was detected during the medical that he took in Madrid on May 28.
"The player has taken this decision after being advised by recognised experts in the field, with the coordination of the medical teams of Atletico Madrid and San Lorenzo.
"Those doctors predict a speedy recovery without any complications."
Both Atletico and San Lorenzo confirmed that the transfer, which will see the Champions League finalists pay a reported £6million for the striker, would be finalised once Correa has recovered.