Mohammad Yusouf, secretary for the governor of Nooristan, said the men were found in a house on Saturday after a search by security officials in the Kamdesh district where they were abducted three nights ago.
"We have received reports from the police chief that the three men have been found, but none of the kidnappers has been arrested," he told Reuters.
The abduction was the latest in a series of violent incidents in the approach to 18 September parliamentary polls, the next big stage on Afghanistan's difficult path to stability.
The three men were seized from a villager's house after the end of a voter registration programme in the rugged region.
Yusouf said the victims could not recognise the kidnappers because they had covered their faces, but said they spoke in a local language.
"We suspect al-Qaida or Taliban were behind the kidnappings," Yusouf had said earlier.
A female Afghan election worker was wounded last week in an attack on a voter registration centre in the same district. No group has claimed responsibility for the attack or the abductions.
Separately, a district judge and a senior district official were killed by suspected Taliban militants in two attacks in the southern province of Kandahar, one late on Friday and the other early on Saturday, officials said.
Taliban officials could not be reached for comment about the incidents.
Members of the radical Islamic government ousted by US-led forces in late 2001 have threatened to derail the polls, and warned Afghans against contesting them or registering as voters.