The UN said Sudanese security officials had handed the two – a Nigerian man and a Zimbabwean woman – to the joint UN-African Union mission, Unamid.
The pair, seized at gunpoint in Darfur on 29 August, were freed after negotiations led by community leaders.
The Sudanese foreign affairs ministry said no ransom had been paid.
Kidnapping was almost unheard of in Sudan before March of this year.
Then Sudanese President Omar al-Bashir was indicted by the International Criminal Court, for alleged war crimes in Darfur.
Since then several aid workers and peacekeepers have been kidnapped, and humanitarian organisations have scaled back on their work because of the growing threat.
Four aid workers who were taken from Sudan, across the border in Chad and in the Central African Republic are still being held.
Different groups are believed to be responsible, and they usually ask for a ransom.
Source: BBC