His rival, Martin Fayulu, labelled the outcome "an ugly swindle".
In an unusually blunt comment on a foreign election, French Foreign Minister Jean-Yves Le Drian also waded into the controversy, describing the results as "not consistent" with observers' reports.
The son of the Democratic Republic of the Congo's (DRC) veteran opposition leader has won the position that eluded his late father, Etienne, for decades - the African nation's presidency.
The result, announced early on Thursday, means the first electoral transfer of power in 59 years of independence in the DRC. Stability in the vast...
"Having gained. 38.57 percent of the vote, Felix Tshisekedi is provisionally declared the elected president of the Democratic Republic of Congo", said Corneille Nangaa, the head of the Independent National Election Commission (CENI). Opposition and activist groups had urged people to be ready to protest on the streets if the results didn't match "the truth of the ballot boxes".
Domestic election observers say they witnessed serious irregularities on election day and during vote tallying, although a regional observer mission said the election went "relatively well".
But the agreement between the opposition leaders fell apart with Tshisekedi claiming his supporters wanted his name on the ballot.
False results will be taken as a "declaration of war against the people", said Heritier Bono, 25, a motorcycle taxi driver.
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A Cook County State's Attorney representative said officials are "in the process of reviewing and following up on these calls". Kelly won a Grammy in 1997 for "I Believe I Can Fly", and is known for such raunchy hits as "Bump N' Grind" and "Ignition".
Losing candidate businessman Mr Fayulu and ruling party candidate Emmanuel Ramazani Shadary can contest the results. The outgoing president succeeded his assassinated father in 2001 before winning elections in 2006 and again five years later.
President Joseph Kabila is due to step down after 18 years in office.
But one Congolese election observer group, Symocel, on Tuesday reported "major irregularities" including the disappearance of envelopes containing results from almost 120 polling stations in Kinshasa, an opposition stronghold.
Analysts have warned that any widespread perception the election has been stolen could trigger a cycle of unrest, particularly in the eastern borderlands where Fayulu enjoys some of his strongest support.
Meanwhile the influential Catholic Church, which deployed 40,000 observers during the vote, said that it knows who won the election.
The presidents of South Africa and Zambia are urging Congo's electoral commission to "speedily" complete vote-counting and announce the delayed results of the December 30 presidential election.
While Nshole acknowledged the difficulties in manually counting votes, especially in remote areas, he warned that the longer the election results are delayed, the more that suspicion will grow among the Congolese people.