"Our club has reached agreement with San Lorenzo on the transfer of the young Argentine talent," Atletico said in a statement on their website (www.clubatleticodemadrid.com) late on Tuesday.
"The young footballer is known for his speed, talent and ability, which have made him one of the attacking reference points for his team, for whom he has scored eight goals this season," added the Champions League runners-up.
Atletico are facing a summer of transition after a sensational season when they won their first La Liga title in 18 years and lost to city rivals Real Madrid in the final of Europe's elite club competition.
Several players who have impressed under Argentine coach Diego Simeone, including top scorer Diego Costa, midfielders Koke and Arda Turan and defender Miranda, were targets for wealthier clubs, according to Spanish media.
Correa, 19, who hails from Lionel Messi's home town of Rosario, has helped favourites San Lorenzo reach the Libertadores Cup semi-finals, which will be held after the conclusion of the World Cup finals in Brazil in July.
- Sports & Recreation