A judge who investigated the disappearance has previously said the submarine, which was built in the German seaport of Emden in 1983 before completing an update in Argentina in 2013, had "many flaws".
Earlier in the morning, the navy said a "positive identification" had been made by a remote-operated submersible from the American company Ocean Infinity.
The wreckage of the ARA San Juan, which "suffered an implosion", was found about 870 meters (2,850 feet) down on the ocean floor, Argentine naval Capt. Gabriel Attis later told reporters in Buenos Aires.
The stunning news, which has been confirmed by the Defence Ministry, the Navy and the United States firm leading the search for the vessel, arrived in the early hours of Saturday morning. "They say that our youngsters are inside", she said. The company was responsible for the search for the missing vessel and was commissioned by the Argentine government.
The San Juan was returning to its base in the coastal city of Mar del Plata when contact was lost after it reported an electrical fault.
This week, relatives of the lost crew held a commemoration service for the dead seamen just two days before the sub was found.
Aguad said: "Much of what happens from here will have to be resolved by the justice department".
The first anniversary of the submarine's disappearance was marked with an event at the Mar del Plata naval base on November 15, with President Mauricio Macri in attendance.
The short circuit was caused by seawater entering the vessel's "snorkel", a tube that reaches the surface to refresh the vessel's air and recharge the batteries, the captain said in a call to his commander on land. President Mauricio Macri attended and promised to keep up the search for the submarine.
It had set out in September on the latest attempt to find the San Juan, whose disappearance cost the navy's top officer his job. The navy said the blast could have been caused by a "concentration of hydrogen" triggered by the battery problem reported by the captain.
"Our thoughts are with the many families affected by this bad tragedy".
Over a dozen worldwide partners including the USA helped the Argentine Navy search for the ARA San Juan for weeks, though the search was stymied by rough weather and was eventually called off it became increasingly unlikely that any crew could have survived.