Argentinian Correa will join from San Lorenzo pending the successful completion of a medical and has signed a five-year deal with the Spanish champions.
Atletico also enjoyed an excellent season on the continental front, only losing Saturday's UEFA Champions League final to city rivals Real Madrid after extra time.
Correa is highly rated and has reportedly cost the Madrid club a fee in the region of €8 million.
An Atletico statement read: "Our club has reached an agreement with San Lorenzo de Almagro for the transfer of the young Argentinian talent, pending the corresponding medical check-up.
"Afterwards, the forward will commit to our club for five seasons.
"Angel Correa arrived at San Lorenzo when he was only 12 years old, after having been in the Alliance Sport and Tiro clubs, making his debut in the top flight last year.
"The young footballer is noted for his speed, talent and ability, which have led him to be one of the offensive leaders of his team, with which he's scored eight goals in this campaign."
