Despite threats from jihadi groups, no violence was reported during the first round of voting on Sunday and observers put turnout at about 50 per cent in a country where it has never been over 38 per cent.
Even in Kidal, the Tuareg stronghold in the north of the country, there were no violent incidents, although turnout there was reported to be as low as 12 per cent.
Hollande was the first foreign head of state to comment on the vote.
“This election confirms Mali’s return to constitutional order after the victory won over the terrorists and the liberation of the territory,” he said in a statement issued on Sunday night.
Prime Minister Jean-Marc Ayrault, in Malaysia on an official visit, also claimed France’s share of the glory.
But he tried to dissociate the Serval military intervention from the traditional Françafrique policy, which is often criticised as neo-colonial.
"For France, it is a great success,” he said. “Our international partners have hailed our courage and coherence because France in no way wanted to do anything reflecting the militarism and paternalism of the past, but on the contrary to give Africa and in this case Mali every chance to become a democratic independent nation, in charge of its own development."
With the Socialist government dogged by economic crisis at home, party leader Harlem Désir joined in the cheering, hailing Hollande’s “determination” when he gave the order for the Serval mission to take place.
The US on Monday congratulated Mali’s leaders for the smooth conduct of the poll.
Official results will not be available until 2 August but exit polls by Malian journalists showed former prime minister Ibrahim Boubacar Keïta ahead.
As his supporters flooded the headquarters of his Rassemblement pour le Mali to celebrate, his main rival, Soumaïla Cissé, insisted that a second round would be “indispensable and inevitable”.