The announcement, made overnight, sparked accusations of an electoral coup from runner-up Martin Fayulu.
France said the figures did not match results collated on the ground by monitors from the Catholic Church.
The ruling party has not contested the result, sparking accusations of collusion with the Tshisekedi team.
Mr. Tshisekedi’s campaign team has denied these claims saying these are false accusations.
If confirmed, Mr. Tshisekedi will be the first opposition challenger to win since DRC gained independence in 1960. Current President Joseph Kabila is stepping down after 18 years in office.
The capital Kinshasa and other key cities appeared calm on Thursday, but fears remain that the announcement of the result could trigger violence
The full results were, with turnout reportedly 48%:
- Felix Tshisekedi – 7 million votes
- Martin Fayulu – 6.4 million votes
- Emmanuel Shadary – 4.4 million votes
The election outcome was initially expected to be announced on Sunday. The interim result can still be challenged.
Mr. Tshisekedi vowed to be the president of all DR Congolese, saying: “No-one could have imagined such a scenario whereby an opposition candidate would emerge victoriously.”
He struck a conciliatory tone with Mr. Kabila when addressing supporters at his Union for Democracy and Social Progress party headquarters in Kinshasa.
“I pay tribute to President Joseph Kabila and today we should no longer see him as an adversary, but rather, a partner in democratic change in our country,” he said.
A spokesman for Mr. Shadary, who had been Mr. Kabila’s hand-picked candidate, accepted the defeat, saying “the Congolese people have chosen and democracy has triumphed”.