The Italian foreign ministry had announced the release on Friday, but officials in Khartoum denied that it had taken place.
The charity pulled nearly all of its personnel out of Darfur following the abductions. Only staff working on securing the release of their colleagues had remained behind.
Christopher Stokes, general director of the Belgian section
of MSF, said: "We are incredibly relieved that our colleagues are safe and in good
"Their families have been informed and are overjoyed. Our thoughts
are with each of our colleagues and their families as they look forward to
being reunited. We are delighted this incident is resolved."
Aid groups expelled
The abductions came days after the government told the French and Dutch contingents of MSF to leave Darfur.
Khartoum accuses the aid groups of co-operating with the International Criminal Court (ICC) in The Hague, which has indicted Omar al-Bashir, the Sudanese president, for war crimes and crimes against humanity in Darfur over the past six years.
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 the western region from the combined results of war, famine and disease over the course of the last six years. At least 2.7 million have been displaced.