The bishops' conference had also commissioned 40,000 election observers, who were sent to polling stations across the country to report on the election process.
In a Dec. 31 statement, the bishops' conference had voiced concern about voting irregularities, including registered voters who were turned away from polling stations because their names were not on voting lists and election observers being expelled from polling stations by police officers.
Other election observers also reported irregularities including voting machine malfunctions, polling stations opening late, locations being changed on short notice, and an inability to cast votes privately, according to the BBC.
The bishops' conference had delayed the release of its preliminary observation after internet connections and text message services were shut down across the country on Dec. 30.
More in Middle East - Africa
Reuters has reported that observers from France and Belgium have also voiced doubts that Tshisekedi won the election, and three diplomats who had reviewed the Church's observer mission data said Fayulu had won.
In his first remarks after his victory was announced, Tshisekedi promised to work closely with Kabila, AFP reported.
Tshisekedi, 55, leads the Union for Democracy and Social Progress, the country's oldest and largest opposition party.
The 2018 election was a major test for the volatile nation, which has been plagued by political corruption, instability, and violence, and has never seen a peaceful transition of power since it gained independence in 1960.
At least four people have been killed so far in scattered protests of the election results.