Ali Ahmed Karti told Hungary's János Martonyi that Papp is in good health and is on his way to Cairo, a statement from the Hungarian Foreign Ministry said.
Martonyi thanked the Sudanese authorities for their assistance in facilitating the release of the Hungarian hostage.
Papp, a retired lieutenant-colonel, who was participating in UN operations to demobilise child soldiers in the province, was taken hostage by gunmen in his home in El Fasher on October 7.