Seven paintings that were temporarily on display at the Kunsthal Museum in Rotterdam were stolen in 2012 in a raid that lasted only three minutes, in what the Dutch media called "the theft of the century".
A court in the Romanian capital ordered the heist's mastermind Radu Dogaru, his mother Olga, Eugen Darie and Adrian Procop to reimburse the paintings' insurers.
Prosecutors put the total value of the haul at over 18 million euros (over $24 million) while art experts at the time of the heist had claimed the paintings were worth up to 100 million euros.
Olga Dogaru told investigators she burned the paintings in her stove in the sleepy village of Carcaliu in eastern Romania in a bid to protect her son when he could not sell them.
She later retracted the statement but a separate investigation is under way to determine if the masterpieces did end up in ashes.
Ernest Oberlander-Tarnoveanu, director of Romania's National History Museum, said evidence of "painting primer, the remains of canvas and paint" were found in the stove, but experts must determine whether the ashes came from the missing paintings.
The works include Monet's "Waterloo Bridge, London" and Picasso's "Harlequin Head". None of them was equipped with an alarm.
"We will contest the ruling," Catalin Dancu, the Dogarus' lawyer, told AFP.
"In the first place, we don't believe the stolen paintings were the originals and secondly it is up to the museum to pay because it took the stupid risk of displaying the artwork without a proper surveillance system," he added.
The paintings had been loaned to the museum for a show to celebrate its 20th anniversary by the Triton Foundation, which was set up to look after the art collection amassed by the Dutch investor Willem Cordia, who died in 2011.
The canvases were transported to Romania hidden in pillowcases and prosecutors think they were destroyed after a failed attempt to sell them.
Radu Dogaru, 30, who admitted planning the heist, was sentenced to six years in prison in February, and his accomplice Darie to five years and four months.
On Monday, Procop was handed a sentence of four years and eight months while Dogaru's mother was jailed for two years.