The Coalition for Change faced many political opponents at the polls.
The Kabila family has led Congo for more than 20 years.
Vast, poor and burdened by a history of bloodshed, the DRC is in the grip of a two-year-old crisis over the succession of President Joseph Kabila.
He has vowed to be "the president of all DR Congolese", saying: "No-one could have imagined such a scenario whereby an opposition candidate would emerge victorious". Britain, France and Belgium, the former colonial power, all expressed concerns. Tshisekedi supposedly got the qualification from the Institute of Commercial Careers in Brussels.
Tshisekedi "is provisionally proclaimed elected as president", CENI President Corneille Nangaa said.
His party knows how important the qualification issue is.
"There's no spirit of revenge", said Tshisekedi.
Police installed metal barriers and blocked traffic outside the electoral commission as it continued meetings that began late Tuesday.
Opposition candidate Martin Fayulu wipes his face before speaking to the press at his headquarters in Kinshasa, Congo, Thursday, Jan. 10, 2019. He will have a lot of influence in determining what happens next.
Fayulu, who once tweeted that "When the wicked beareth rule, the people mourn", was backed by two popular opposition figures barred from running, former Vice President Jean-Pierre Bemba and former governor Moise Katumbi.
For a long time, Fayulu was ahead in the opinion polls in front of both Shadary and Tshisekedi.
The church, which has long pressed for a fair election in the largely Catholic nation, refused to name its "clear victor".
Two diplomats also said all major observation missions, including those of the African Union and the Southern African Development Community, showed similar results to those of the Catholic church. Releasing untrue results would be considered a "constitutional coup d'etat", said Carbone Beni, coordinator of the Filimbi movement, calling on other African nations to make sure the people's vote is respected.
South Africa urged the DRC to quickly certify the results and move past the election, while the European Union seems nervous about either endorsing or challenging the outcome.
The global community has not congratulated Tshisekedi on his victory. Some said they would be happy as long as Fayulu or Tshisekedi won, recalling the violence that followed past disputed elections. He has suggested that the front may have thrown its weight behind Tshisekedi and pushed him to victory.
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. Tshisekedi's pick for prime minister, Kamerhe, has affirmed this.
According to the BBC, the Catholic Church is privately inclined to doubt the results but might not challenge them as strongly as Fayulu would like, because they are wary of "public demonstrations".
Any widespread perception the election has been stolen could set off a destabilizing cycle of unrest, particularly in the volatile eastern borderlands where Fayulu enjoyed some of his strongest support.
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