A third piece they stole, a pen and ink drawing by 16th-century Italian painter Guglielmo Caccia, is still missing. The burglars also dropped a fourth painting, also by Mondrian, as they fled.
Police recovered the two carefully packaged paintings from a dry, sandy underground cave near the town of Keratea, about 45km southeast of Athens.
Footage of the crypt-like hiding spot broadcast on state TV showed several small entrances dug into the side of a ravine obscured by lush Mediterranean vegetation.
The paintings are believed to have been moved to the dark, dusty location several months ago.
A 49-year-old Greek man has been arrested in connection with the theft.
Picasso painted the portrait of his partner and muse, Dora Maar, in 1939. Ten years later, he offered it as a gift to the Greek people for their resistance against the Nazi occupation in World War II.
An inscription written in French by the artist on the back reads "For the Greek people, Tribute from Picasso."
"Picasso's painting carries special weight and value for the Greek people as Picasso dedicated it to their struggle against the fascist axis and it bears the handwritten signature of the painter," said Mendoni.
"That is why the painting is impossible to sell and exhibit as it is completely identifiable as a product of theft from the National Gallery."
"The National Gallery is now healing its greatest wound," she added.
The National Gallery of Greece is the largest repository of Greek art in the country and boasts over 20,000 priceless other works, thanks in part to the donation of the collection of Alexandros Soutzos, a jurist and collector.
It closed for renovation in 2012 shortly after the remarkable theft and recently reopened to the public in May after a €59m expansion and renovation – including an overhauled and updated security system.