Senegal's ruling coalition candidate Amadou Ba has called the opposition's Bassirou Diomaye Faye to concede victory in Sunday's presidential election, a government official said.
Unofficial results showed that Mr Faye had a strong lead over Mr Ba.
Mr Faye had been in prison 10 days before the vote and campaigned on the promise of radical change.
Official results from an election which was originally due last month are expected in the coming days.
The vote followed months of political turmoil in one of Africa's most stable democracies, after outgoing President Macky Sall tried to postpone the election until December.
Several of the other 15 candidates had already conceded.
President Sall has also congratulated Mr Faye and said that it was a win for the people of Senegal.
Mr Faye, who turned 44 on Monday, ran as an independent. But he had been a senior member of the dissolved Pastef party, led by Ousmane Sonko, the popular figure who many thought would succeed Mr Sall.
But Mr Sonko was disqualified from the election because of a defamation conviction, which he said was politically motivated. Mr Sonko backed Mr Faye's bid for the presidency.
The first set of results announced on television overnight showing that Mr Faye had won a majority of the votes counted up to that point triggered celebrations in the capital, Dakar.
In the streets, young people were dancing, singing, waving the Senegalese flag and honking their cars horns.
In Ndiaganiao, Mr Faye's hometown 80km (50 miles) east of Dakar, residents were seen congratulating each other as if to express this as a victory for the whole community.
After experiencing one of its worst political crises, for many this victory symbolises hope for Senegal's future.
