Mr Zelenskiy appears to have won with 73% of the vote. Before entering politics the comedian was best known for playing the president in a hit television sitcom.
His opponent, incumbent leader Petro Poroshenko, conceded on Sunday evening after winning just 25.3% of the vote.
Mr Poroshenko will leave office in May after five years as president.
He said he did not plan to leave politics completely.
Throughout the campaign he had attempted to portray himself as a champion of Ukrainian identity.
Bur Mr Zelenskiy won twice as many votes as his opponent in the first round of the election three weeks ago, reflecting public anger at endemic corruption and a struggling economy.
The comedian has promised to end the war in the eastern Donbass region and to root out corruption, amid widespread dismay over rising prices and falling living standards.
He has pledged to keep Ukraine on a pro-Western course, but has suggested the country needs to hold a nationwide referendum on whether to join Nato.
During the campaign Mr Poroshenko had warned against electing a president with no political experience.
“It could be funny at first, but pain may come later,” he said.
Additional reporting by agencies