The second-place victor, Fayulu, has not yet indicated whether he will contest the results. He called the official result a "robbery" and asked supporters to "rise as one man to protect victory".
The Enough Project, a US policy group that focuses on Africa, wants the global community to closely scrutinize the results, and take action if they are found to be rigged. 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.
Fayulu can appeal the results to Congo's constitutional court but has not yet indicated whether he will.
Activist groups urged people to "be ready to massively take to the streets" if results don't match "the truth of the ballot boxes".
Just hours later, the Church said election results tallied by its 40,000 observers scattered across the country showed a different victor, without specifying who.
Mr Tshisekedi, who received more than 7 million votes, had not been widely considered the leading candidate. Long in the shadow of his father, the late opposition leader Etienne, he startled Congo previous year by breaking away from the opposition's unity candidate, Fayulu, to stand on his own.
"This is because a Tshisekedi presidency would be the least bad alternative to a Shadary victory for the regime as it would put a veil of legitimacy on the electoral process and would be more manageable than a Fayulu presidency", she said.
The Chairperson of the Commission reiterates his congratulations to the people, political actors, civil society and the relevant national institutions of the Democratic Republic of the Congo for the conduct of the elections under conditions deemed satisfactory by the African Union Election Observation Mission led by President Dioncounda Traoré. More importantly, perhaps, he also has the backing of political heavyweights Jean-Pierre Bemba and Moise Katumbi, both forced into effective exile overseas and unable to contend the polls.
Apart from the fact that majority of the observers expected the authorities to favour the anointed candidate of the president, Joseph Kabila - who picked Emmanuel Ramazani Shadary to be his successor; there is increased concern over the position of Martin Fayulu, another opposition candidate who had a healthy lead in pre-election polling.
The UN security council is due to meet today to discuss the situation.
The announcement of an opposition win was a shock as many had expected the results to be stacked in Shadary's favour, prompting heavy worldwide pressure on Kinshasa to respect the wishes of the electorate.
Patta said the country hasn't seen a peaceful transition to power since Belgian rule ended in 1960. Dozens of polling centers opened hours late as materials went missing.
"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.
Congo's government cut internet service the day after the vote to prevent speculation on social media.
However, most parts of the country appear to be calm.
Some Congolese tired of Kabila's 18-year rule, two turbulent years of election delays and years of conflict that killed millions of people said they simply wanted peace.
Corruption fighter Mr Fayulu finished second in the vote.
He is barred from serving three consecutive terms, but during more than two years of election delays many Congolese feared he'd find a way to stay in office.