A day earlier, three members of a Russian aircrew working for the private Sudanese Badr Airlines were kidnapped in Darfur's largest town, Nyala, and Sudan's army said it was searching for the men.
Flavia Wagner, 35, was working for US charity Samaritan's Purse in Darfur. She arrived in Khartoum on Monday looking thin but smiling as she emerged from the plane.
"We thank God that Flavia is safe and free," said Franklin Graham, president of Samaritan's Purse.
The US charge d'affaires in Sudan, Robert Whitehead, thanked the government for securing her release but said of the kidnappings: "It is an ongoing problem that will have to be addressed."
Abductions are carried out mostly by young men from Arab tribes who demand ransoms. Khartoum has yet to prosecute any kidnappers and reports of ransoms being paid in the past have added to the problem.
Wagner's kidnappers, who originally demanded a ransom, told Reuters they released her to the South Darfur authorities without being paid any money.
"We have demands from the government like developing our areas — we want hospitals, education — if these demands are met these kidnappings will no longer happen," one of the kidnappers, Abu Mohamed Al-Semeh, said by satellite phone.
During the last month of her kidnap ordeal, Wagner told Reuters her conditions had become desperate, sleeping under a tarpaulin in heavy rain with 20 armed men and drinking only camel's milk.
She said her kidnappers, who at first had treated her well, had begun to threaten her physically in the final weeks.
Russia's Foreign Ministry said the three kidnapped members of the aircrew — pilot, co-pilot and engineer — were abducted in a minibus in which they were traveling.
"According to preliminary information, the crew is being held in the town of Nyala and has not been taken outside of the town," the Russian ministry said in a statement.
The abductions have been directed at foreign aid workers and UN-African Union (UNAMID) peacekeepers since the International Criminal Court issued an arrest warrant for President Omar Hassan Al-Bashir last year for war crimes and crimes against humanity.
Bashir denies the charges against him and responded by expelling 13 of the largest aid agencies working in Darfur helping 4 million people in one of the world's most serious humanitarian crises, accusing them of giving information to the court.
The ICC added genocide to charges against Bashir this year and seven aid workers have since been told to leave Darfur.
