Tshisekedi's victory was greeted by celebrations at the headquarters of the Union for Democracy and Social Progress (UDPS), the country's oldest and largest opposition party which was founded by his late father, Etienne, a former minister under the late dictator Mobutu Sese Seko who then became an opposition leader and a thorn in Mobutu's side for years.
Leading opposition candidate Martin Fayulu, a Kinshasa lawmaker and businessman, has urged the electoral commission to announce the true results as quickly as possible and warned it not to "play with fire, it is very risky".
Last week CENCO called on the election commission to publish results "in keeping with truth and justice", adding that data in its possession pointed to a clear victor.
Anti-riot police with water cannon and armored vehicles are outside Congo's electoral commission ahead of the announcement of the first results of the presidential election.
It was not clear whether Fayulu would dispute the election results in court.
The delayed results came after global pressure to announce an outcome that reflected the will of the people.
Fayulu, told RFI that the results were an "electoral coup", adding that the provisional results "have nothing to do with the truth at the ballot box".
Fayulu alleges that President Joseph Kabila engineered a backroom deal with the largely untested Tshisekedi in order to thwart anti-corruption efforts in a country with staggering mineral wealth.
Attention turns to Congo's powerful Catholic church, which has said its 40,000 election observers at all polling stations found a "clear winner" but was barred by electoral regulations from saying more.
A CENI source and a diplomat said they expected results to be announced later on Wednesday.
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.
Many have seen this election as Congo's first chance at a democratic, peaceful transfer of power since independence in 1960.
Congo on December 30 voted for a successor to departing President Joseph Kabila.
South Africa and Zambia, DRC's neighbour to the south, joined the clamour to publish the results. "Mr Fayulu was in principle the leader to come out of these elections".
The statement says South African President Cyril Ramaphosa and Zambian President Edgar Lungu warn that the delay in releasing results "can lead to suspicions and compromise peace and stability of the country".
The bloodshed revived traumatic memories of the DRC's brutal past. Barred by the constitution from seeking a third term, Kabila handpicked Shadary, a loyalist former interior minister, to run for the ruling Common Front for Congo coalition, fueling suspicions the current head of state meant to retain considerable influence over his preferred successor.
Bloody clashes marred elections in 2006 and 2011, and two wars between 1996 and 2003, drawing in armies from around the region, claimed millions of lives.
"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.
But on Tuesday, the opposition hinted at a rapprochement.
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.
Opposition presidential candidate Felix Tshisekedi casting his ballot in Kinshasa. He has a place here in Congo.