The 1882 "Seascape at Scheveningen" and 1884/85 "Congregation leaving the Reformed Church at Nuenen" were "recovered during a massive, continuing investigation... conducted by a specialized team investigating organized crime," the museum said in a statement.
"The curator who inspected the authenticity and provenance of the works at the request of the Italian Public Prosecutions Department drew a firm conclusion: 'they are the real paintings!'," the museum added.
Despite a 14-year journey, the two paintings by Vincent van Gogh "appear to be in fairly good condition," it said.
Dutch police opened an international hunt back in 2002 after thieves apparently used a simple ladder and a length of rope to steal the two works, worth millions of dollars.
The criminals broke into the museum in downtown Amsterdam on December 7th that year using the ladder to climb onto the roof, where they broke through a window and used a rope to get in and out of the heavily fortified building.
The daring heist left Dutch police flabbergasted at the time. The paintings' whereabouts were unknown until being recovered in the Naples area, the Van Gogh Museum said.
"After all those years you no longer dare to count on a possible return," said the museum's director, Axel Rueger, who has travelled to Naples to view the missing Vincents.
"The paintings have been found. That I would ever be able to pronounce these words is something that I no longer dared to hope for," he said.
It was unclear when the paintings were to return to Amsterdam, as they were used as proof in an ongoing investigation in Italy, the museum said.