Papastathopoulos, 23, could join the Bundesliga side on a permanent deal at the end of the season if he impresses at the Weserstadion.
General manager Klaus Allofs said: "He is a young player who with Genoa and Greece has already gained some experience.
"With his speed, strength and tackling he will certainly help us."
The defender emerged from the academy at AEK Athens and after joining Genoa in 2008 spent last season with AC Milan.
Papastathopoulos added: "After initial discussions with Klaus Allofs and (coach) Thomas Schaaf it was immediately clear that I would accept the offer from Werder.
"Now I will try to integrate as soon as possible into the team."