Tshisekedi, 55, is the head of country's oldest and largest opposition party the Union for Democracy and Social Progress (UDPS), founded by his father Etienne - a major Congolese political figure.
The DRC - a vast and poor country burdened by a history of bloodshed - has been in the grip of a two-year crisis over the succession of President Joseph Kabila, who said last year he would finally step down after almost two decades as leader. "The son is very limited", Valentin Mubake, former secretary-general of Tshisekedi's party told the Guardian last month.
"Felix is more diplomatic, more conciliatory, more ready to listen to others".
He took over from his assassinated father Laurent in 2001. However, he has never held high office or even a managerial role, and his Belgian professional qualifications have been questioned by opponents.
During his campaign he promised a return to the rule of law, to fight the "gangrene" of corruption and to bring peace to the east.
Mr Tshisekedi, 56, will replace President Kabila, who has ruled the country for 18 years.
"How long are we going to negotiate results?" he asked.
French Foreign Minister Jean-Yves Le Drian dismissed Tshisekedi's victory as "not consistent" with the actual results, indicating that Fayulu had won.
Many analysts have warned that an implausible or rigged election could trigger an eruption of violence in Congo's streets.
"The Secretary-General calls on all stakeholders to refrain from violence and to channel any eventual electoral disputes through the established institutional mechanisms in line with the DRC's Constitution and relevant electoral laws", said Mr. Guterres in a statement released by his Spokesperson, late on Wednesday evening in NY.
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Kabila, 47, was due to step down two years ago but clung to office, sparking widespread protests that were repressed at the cost of scores of lives. And the long-delayed election has heightened fears that any outcome would not be perceived as free and fair.
The provisional results put candidate Felix Antoine Tshisekedi Tshilombo ahead of Martin Fayulu Madidi and Emmanuel Shadary.
Tshisekedi's academic qualifications are important because the DRC's electoral commission requires that every presidential candidate must have either a postgraduate diploma, or at least five years' experience in politics, administration, or socio-economy. Shadaray came third with 23.8%. There were other organisations monitoring the elections, such as the Southern African Development Community, but it isn't clear yet if they agree or disagree with the electoral commission's provisional election results.
But the outcome was swiftly denounced by Fayulu as a sham.
While bishops stopped short of publishing their own results or saying who they believed was the true victor, they made clear it wasn't Tshisekedi, as declared by election commission CENI. "It's an ugly scam by Nangaa and his political cronies".
"We will never accept this nomination". The biggest team of independent observers, from the country's influential and widely trusted Catholic Church that deployed observers at 40,000 voting stations, confirmed on Thursday that its own data showed Mr. Tshisekedi losing the election.
"The delay in releasing the results of the elections can lead to suspicions and compromise peace and stability of the country", South African President Cyril Ramaphosa and Zambian counterpart Edgar Lungu said in a joint statement. Although it did not name the victor, its announcement drew a sharp rebuke from the ruling coalition.
By breaking away from the opposition coalition supporting Fayulu, Tshisekedi "positioned himself to bargain with the regime", Englebert wrote.
"Kabila did not want to risk announcing Shadary as the victor, which would have triggered violent protests and worldwide condemnation".
Tshisekedi's camp has acknowledged contact with Kabila's representatives since the election but said they were aimed at ensuring a peaceful transition and denied a deal.
"Mr Kabila can not stay and make an arrangement with someone who will not have any power".