MSF had earlier said on Friday that the trio had been released, after receiving such assurances from the Sudanese government.
The Italian foreign ministry had also confirmed the release on Friday.
MSF pulled nearly all of its personnel out of Darfur following the abductions. Only staff working on securing the release of their colleagues have remained behind.
The abductions came days after the French and Dutch contingents of the MSF were told to leave Darfur.
The Belgian foreign ministry said that none of its nationals were involved.
Aid groups expelled
Khartoum accuses the aid groups of co-operating with the International Criminal Court (ICC) at the Hague, which says that Omar al-Bashir, the Sudanese president, led a violent campaign in Darfur over the past six years.
MSF branches are among 13 aid groups ordered to leave Sudan after the ICC issued an arrest warrant for al-Bashir for alleged war crimes in Darfur.
The United Nations says that more than 180 foreign aid workers have left Sudan since the order by Khartoum to expel the aid groups.
The conflict in Darfur erupted after ethnic fighters rebelled against the Arab-dominated government.
The UN estimates that about 300,000 people have died in Darfur from the combined results of war, famine and disease over the course of the last six years and at least 2.7 million have been displaced.