Hilda Kawuki and Sharon Commins are "unharmed and healthy," said GOAL, the Ireland-based charity they work for.
The head of GOAL, John O'Shea, said there was "a sense of overwhelming relief and joy" at the release of the women, who had been held since July 3.
"We are especially happy and pleased for the families of both Hilda and Sharon who have suffered so much... Their happiness must know no bounds," he said in a statement.
Kawuki is from Uganda and Commins is Irish, GOAL said.
"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.
They are expected to fly to Khartoum, Sudan's capital, later on Sunday, before continuing to their respective homes.
O'Shea said no ransom had been paid.
Their release comes after Ireland's foreign minister met top Sudanese officials in September to press them over the kidnapping of the Irish aid worker.
Darfur has seen a wave of hostilities toward foreign aid workers and escalated kidnappings in recent months.
Sudanese President Omar al-Bashir ordered the expulsion of aid groups earlier this year after he was indicted by the International Criminal Court on charges of war crimes.
Violence in Darfur erupted in 2003 after rebels began an uprising against the Sudanese government. To counter the rebels, Arab militias with ties to the government went from village to village in Darfur, killing, torturing and raping residents, according to human rights organizations.
Nearly 300,000 people have been killed in the conflict in Darfur, and more than 3 million displaced, the United Nations estimates.
GOAL, which was founded in 1977, has worked in Darfur for 23 years, the agency said.
