The 23-year-old, who left Anfield in 2010 without making a single first-team appearance for the Reds, had spent last season on loan at RKC Waalwijk and was deemed surplus to requirements upon his return to Greece.
"I am very happy that I can play for Roda JC," Nemeth told the club's official website. "Besides the fact that I have already worked with the coach, I have also made this choice because of the club.
"There is a strong team here and in the past many Hungarians have played here."
Nemeth has been capped five times by Hungary at senior international level.