It is unclear whether voting will ever be held in parts of eastern Congo where the election was delayed - disenfranchising more than 1.2 million people - due to concerns about Ebola and violence.
On November 11, Tshisekedi joined six other opposition leaders to rally behind a single unity candidate, Martin Fayulu, to take on Kabila's handpicked successor, Emmanuel Ramazani Shadary.
The Catholic Church's bishops conference said last week that it knew the identity of the victor and demanded that CENI publish accurate results.
Mahamat has also called on all concerned stakeholders to act in a way that consolidates democracy and preserves peace in the country, as they wait for the final official results.
Tshisekedi, meanwhile, whose victory was declared at about 0200 GMT paid his respects to outgoing President Joseph Kabila, and described him as a "partner in democratic change". Last week the bishops said their observations showed a clear victor - although they did not name Martin Fayulu, the other opposition frontrunner - as that candidate.
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Foreign Minister Jean Yves Le Drian told French TV the announcement "did not conform" with other results, notably those produced by Congo's Catholic church which he described as totally different. "In 2006, Jean-Pierre Bemba's victory was stolen, in 2011 Étienne Tshisekedi's victory was stolen".
According to news reports, the preliminary results announced by the independent electoral commission, known by its French acronym, CENI, which declared opposition candidate Felix Tshisekedi the victor of the 30 December election, do not tally with the unofficial figures gathered by independent poll observers.
The victor received 7,053,000 out of the 18,280,830 ballots considered valid, Nangaa said in presenting the preliminary results.
Earlier Thursday the country's electoral commission presented a delayed provisional count, naming Tshisekedi the victor with 38.57 per cent of the vote.
According to the official figures published by the electoral commission, Tshisekedi won the elections by 38%, four points ahead of Fayulu - who had a 20-point lead ahead of Tshisekedi before the elections.
"On the face of it, Mr Fayulu was the leader coming out of these elections", he said.
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Kabila has ruled since 2001 in the troubled nation rich in the minerals key to smartphones around the world.
The delayed results, almost two weeks after the December 30 vote, came after worldwide pressure to announce an outcome that reflected the will of the people.
The election would be the nation's first successful democratic exercise since it achieved independence from Belgium in 1960. Dozens of polling centers opened hours late as materials went missing. "This is the beginning of national reconciliation".
DR Congo's government cut internet services the day after the vote to prevent speculation on social media.
"Kabila will be able to influence Tshisekedi, who now owes his ascendancy to power to Kabila's control of the electoral commission", Mr. Besseling told AFP.
The current president, Joseph Kabila, is stepping down after 18 years in office.
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Speaking to thousands of cheering supporters in the capital Kinshasa, Tshisekedi said he would be the president "of all Congolese".