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.
