French Defence Minister Florence Parly tweeted the announcement on Monday, describing the discovery as a "relief and technical feat".
Fifty-two sailors were on board the Minerve when it vanished near the port of Toulon, on the French south coast, in January 1968.
Previous efforts to find the submarine were all unsuccessful.
Ms Parly announced the new recovery effort earlier this year, following fresh requests from bereaved families to find their loved ones.
"We have just found the Minerva," Ms Parly tweeted (in French). "It's a success, a relief and a technical feat. I think of the families who have been waiting for this moment so long."
The new search team reportedly re-analysed data from the accident, including tides, to help find the wreckage with the help of new technology, AFP reports.
The final discovery was made by a boat belonging to private US company Ocean Infinity, an unnamed French naval official told the news agency.
The missing submarine was found 45km (30 miles) from Toulon 2,370m (7,800ft) under the surface, AFP reports.
The precise reason behind the accident involving the Minerve has never been revealed.
It was one in a string of a deadly disasters involving military submarines around the world during the 1960s.