At a news conference, police said both paintings were in better than expected condition, and were recovered in a police operation.
The paintings were stolen in a bold, daylight raid from the Munch Museum in Oslo on Aug. 22, 2004.
"The pictures came into our hands this afternoon after a successful police action," said Iver Stensrud, head of the police investigation. He said the police had been working intensely for two years to find the paintings.
He said no reward had been paid.
"All that remains is an expert examination to confirm with 100 percent certainty, that these are the original paintings. We believe these are the originals," Stensrud said.
"The Scream," which shows a waif-like figure apparently screaming or hearing a scream, has become a modern icon of human anxiety.
"I saw the paintings myself today, and there (was) far from the damage that could have been feared," said Stensrud.
Stensrud said it was not possible for the news media, or the public, to immediately see the paintings. He also refused to discuss the methods or details of the search.
Oslo's Munch Museum expressed delight over the national treasures being recovered.
"I am almost crying from happiness," said Gro Balas, who chairs the Munch Museum board.
"They have been given a cursory examination, but for now I am content just to feel overjoyed," she said. "The word we have about their condition is reassuring."
The paintings had remained missing despite the conviction of three suspects in the case in May, an international police hunt and the offer of a $294,000 reward by the City of Oslo, which owns the paintings.
Stensrud said those convicted had not contributed to the recovery of the paintings. He also said police believe the paintings had been in Norway the whole time.
"We feel we have been hot on the trail of the paintings the whole time, but it has taken time," he said.
In May, three Norwegians were sentenced to prison in the case by the Oslo District Court, but the masked gunmen remain at large.
Petter Tharaldsen, 34, was convicted of driving the getaway car and sentenced to eight years in prison. Bjoern Hoen, 37, was sentenced to seven years in prison, and Petter Rosenvinge, 38, to four years for their roles in providing and preparing the getaway car.
Tharaldsen and Hoen were ordered to pay $120 million in compensation to the City of Oslo.
Munch's emotionally charged painting style became a major influence in the birth of the 20th-century Expressionist movement.
"The Scream" and "Madonna" were part of his "Frieze of Life" series, focusing on sickness, death, anxiety and love.
Painted in 1893, "The Scream" shows a road overlooking Oslo, and the skyline may have been inspired by the fallout from the eruption of Krakatoa 10 years earlier. Also at the time, Munch's sister was in a mental hospital nearby for manic depression.
There are several versions of the painting. The one recovered is tempera on cardboard. There is another copy at the Munch Museum, one at the National Museum in Oslo and a fourth in private hands. Munch later also translated the painting into a lithograph.
There are also several versions of "Madonna," also from around 1893, and, again, the National Museum also has a copy.
The copies of the two paintings belong to the Munch Museum were from the artist's personal collection and were bequeathed to the city of Oslo.
Munch died in 1944 at the age of 80.