"It was a surprise for us and for our troops to be able to free a hostage," he told French television. "We did not have any information about the presence of a hostage."
The commandos who freed him "neutralised the terrorist group" they were targeting, Mr Hollande said. He presented the raid as part of a routine operation by French forces combating militants in West Africa.
France was largely successful in routing an al-Qaeda-linked insurgency in northern Mali two years ago but maintains a 3000-strong force in the region.
A United Nations source said the French "took a lot of risks" to rescue Mr Rijke after realising he was there. Mr Rijke "is doing well under the circumstances", Bert Koenders, the Dutch Foreign Minister, said, adding he was under the care of Dutch embassy staff and soldiers.
About 500 Dutch troops are serving with the UN force in Mali.
"I'm happy and relieved that this terrible period of uncertainty and sadness has been brought to an end," Mr Koenders said.
Mr Rijke appeared in a video released on his 1000th day in captivity five months ago with a French hostage, Serge Lazarevic, the last of 14 French nationals thought to have been held by al-Qaeda in the Islamic Maghreb.
Mr Lazarevic, 51, was released weeks later in exchange for the release of four jihadists from prisons in Mali, the Malian authorities said. The French government denied reports of a ransom payment.
Ransoms have brought Islamist groups tens of millions of pounds and France has often been accused of paying to secure the freedom of its citizens. Paris strongly denies the allegations.
Officially, yesterday's raid marked the first time French forces have rescued a hostage in the region.
When four French hostages were freed two years ago after being kidnapped in neighbouring Niger, a French company was reported to have paid nearly -15 million ($29.6 million).
France was accused of paying -12 million ($23.6 million) for the release of four French journalists in Syria last year.
Uncertain fate
• The fate of two other hostages seized at gunpoint with Sjaak Rijke in November is uncertain.
• A Swede, Johan Gustafson, and a South African, were taken from a Timbuktu hotel in November 2011. A German who tried to resist capture was killed.
• Mrs Tilly Rijke managed to escape capture by hiding in a tent in the roof of the couple's Toyota Landcruiser.
