Libyan state television showed visibly tired but relieved passengers surrounded by Libyan soldiers following their release.
"The night was terrifying and difficult. I thank the Libyan authorities for their efforts which allowed us to be freed," a Sudanese passenger told Jana, the official Libyan news agency.
Another passenger said the hijackers were armed with small calibre pistols.
Sudan called on the Libyan authorities to arrest and deport to Khartoum the "terrorist" hijackers.
"We condemned the hijacking and we have appealed to the international community to condemn it as well," Ali Sadiq, spokesman for Sudan's foreign ministry, told Al Jazeera.
The passengers had reportedly been given water but no food.
Some fainted when the air conditioning failed in the searing desert heat.
The hijackers, who had refused to talk directly with Libyan officials after they were given permission to land, said they belong to the Sudanese Liberation Army (SLA), whose exiled leader Abdel Wahid Mohammed Nur lives in Paris, according to Khaled Saseya, an airport director.
A Libyan official at the World War II-era military airport in Kufra, an oasis in southeastern Libya, had said earlier that the hijackers were continuing to hold the crew and were demanding a flight plan to Paris and fuel.
"We condemned the hijacking and we have appealed to the international community to condemn it as well"
Ali Sadiq, Sudan's foreign ministry spokesman
Mohammed Shlibaq, Libya's civil aviation director, said that two Egyptian members of the UN-led Darfur peacekeeping force, two Ethiopians and a Ugandan were among the passengers, Jana news agency reported.
Jana also reported that several Sudanese officials were among the passengers released by the hijackers, including Yaqub al-Malik Mohamed Yaqub, the tribal affairs adviser at the Provisional Authority in Darfur.
No Darfur movement has claimed public responsibility, but the pilot said "the hijackers claim to have coordinated with him [Nur] to join him in Paris," Kufra airport director Khaled Saseya told Jana, adding that they had demanded a flight plan to Paris and fuel.
Nur, whose group was one of two Darfur movements that first fought against the Arab-dominated government in 2003, denied any involvement.
Ibrahim al-Hillo, an SLA commander, suggested the hijackers could be Nur sympathisers.
"We don't have any relation with that hijacking. Civilians, they're angry, they'll behave like that. They may agree with Abdul Wahid [Nur] but in our structure we have no decision like this to hijack a civilian airplane," Hillo said.
The SLA has fractured into multiple groups headed by different field commanders over the more than five years of war in Sudan's western Darfur region.
The UN says up to 300,000 people have died and more than 2.2 million have fled their homes since war in Darfur erupted in February 2003. Sudan says 10,000 have been killed.
Fighters took up arms against the Arab-dominated Khartoum regime and state-backed Arab militias, fighting for resources and power.
But Nur, whose group was one of two movements that first rose up against the Arab-dominated Sudanese government in Darfur in 2003, denied any involvement.