The ARA San Juan was discovered just two days after families of the missing sailors held a commemoration to mark one year after the sub disappeared on November 15.
It was found 2,625 feet down in waters off the Valdes Peninsula in Argentine Patagonia, a statement said.
The navy said a "positive identification" had been made by a remote-operated submersible from the American ship Ocean Infinity, which was hired for the latest search for the missing vessel.
President Mauricio Macri had said there was an "absolute and non-negotiable commitment" to find "the truth" and promised a full investigation after the submarine was lost.
Federal police raided naval bases and other buildings last January as part of the probe, soon after the government dismissed the head of the navy.
The San Juan was returning to its base in the coastal city of Mar del Plata when contact was lost.
The 34-year-old German-built diesel-electric submarine – which was refitted between 2007 and 2014 – had flagged a breakdown in its batteries.
It said it was diverting its route from the far south of Argentina's Atlantic waters to the navy base at Mar del Plata, where most of the crew members live.
But it didn't issue a distress call and it was unclear if the problem left the vessel without propulsion or unable to surface.
The search began November 16, when there was no more contact.
Argentina gave up hope of finding survivors after an intense search aided by 18 countries, but the navy had continued searching for the vessel.
The sub's disappearance gripped the nation, and President Mauricio Macri visited the relatives – troubled by earlier false hopes – and prayed with them.
Underwater sounds first thought to be the crew banging on the hull were later determined to be something else.
A crack Royal Navy team was among those searching for the stricken sub, joining thousands of troops from the US, France, Germany, Brazil, Chile, Peru, Colombia and Uruguay.
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