"At present, they are being interviewed by the national security of the government of Sudan in Kutum, the town from which they were kidnapped," O'Shea said.
The foreign aid workers are expected to fly to Khartoum, Sudan's capital, later on Sunday, before going home.
It was the third kidnapping of foreign humanitarian workers in Sudan's western region since March, when an international court issued an arrest warrant for Omar al-Bashir, the country's president, on charges of orchestrating war crimes there.
Aid organisations working in Darfur have preferred to work without security from the government or peacekeepers in the region to avoid appearing to be taking sides in the conflict, making them more vulnerable.
The series of abductions, along with Sudan's expulsion of 13 international aid agencies in response to the arrest warrant, struck a blow to the vital aid effort in the desert region.
Fighting has declined in Darfur, but aid agencies say the humanitarian situation remains a pressing problem.
Violence in Darfur started in 2003 after fighters began an uprising against the Sudanese government. Nearly 300,000 people have been killed in the conflict in Darfur, and more than three million displaced, the United Nations estimates.