The country’s opposition has joined France, Belgium and the Catholic Church in denouncing the result as fraudulent.
Even as winner Felix Tshisekedi celebrated, supporters of opposition candidate Martin Fayulu were alleging that outgoing president Joseph Kabila had made a backroom deal to keep him out of office.
“Today I am happy,” Mr Tshisekedi told supporters.
“Happy for the people of Congo. Everyone is celebrating that there is peace. No one could imagine the scenario where an opposition candidate could be victorious.”
Mr Fayulu – an anti-corruption campaigner – called the result an “electoral coup”.
It is feared the chaotic vote could increase violence in the African nation, which has a troubled history of political conflict.
Two people have so far been killed in clashes in one town in the west of the country.
The result decides who will lead the DRC after the departure of Joseph Kabila, who has governed since his father was assassinated in 2011 and has overstayed his term by two years.
During the run up to the results Mr Tshisekedi, who inherited the leadership of the Union for Democracy and Social Progress from his father, said Mr Kabila had nothing to fear if he were to come to power.
Mr Fayulu, however, is backed by the Jean-Pierre Bemba, a former rebel who is one of Mr Kabila’s biggest rivals.
The African Union called for any dispute over the election to be resolved peacefully, though it is feared that increased rhetoric by Mr Fayulu could lead to trouble.
“It is important that any disagreement over the proclaimed results, notably that they did not reflect voters’ wishes, be resolved peacefully, by turning to the relevant laws and through political dialogue between the parties involved,” said AU chief Moussa Faki Mahamat.
French foreign minister Jean-Yves Le Drian said Mr Tshisekedi’s victory was the “opposite of what we expected” while Belgium said it would use its temporary seat on the UN Security Council to seek clarification.
If Mr Tshisekedi’s victory is confirmed in the next 10 days he will become the first leader to be elected in the country since Patrice Lumumba, who was toppled in a coup three months after its independence in 1960.