With nearly all ballots counted, he has 73 per cent of the vote compared to incumbent President Petro Poroshenko’s 24 per cent.
Monitors for the Organization for Security and Cooperation in Europe said the election took place with respect for “fundamental freedoms” and set the stage for a “democratic and orderly transfer of power”.
The first-time candidate, who stars in a TV sitcom about a high school teacher who becomes president almost by accident, appeared to have won in both the west and the east, a rarity in post-Soviet Ukraine.
Mr Zelenskiy campaigned on unifying Ukraine, which is torn by bitter debates over national identity and a bloody conflict with Russia-backed separatists.
The separatist conflict in eastern Ukraine and Russia’s annexation of Crimea are likely to dominate the agenda of a leader with no previous political or government experience.
Mr Zelenskiy, a Russian speaker from central Ukraine, vowed to step up efforts to bring the east back under Kiev’s wing but offered no details on what that entailed.
His campaign adviser, Oleksandr Danylyuk, said the new leader’s team “does not have a magic wand” to deal with the issue of the occupied territories but favours jump-starting talks with Russia via European mediators.
The president-elect’s advisers also reject the idea of the Ukrainian government using force to regain control of the east and of Crimea, Mr Danylyuk said.
Russia seized Crimea in 2014 in a move that Ukraine and almost all of the world views as illegal.
Mr Zelenskiy will also have to face off against Russian President Vladimir Putin, who has ruled his country for nearly two decades, if he wants to mend relations with Moscow.
Although polls predicted the untested comedian’s win, Mr Putin’s spokesman Dmitry Peskov told reporters on Monday it was too soon to congratulate Mr Zelenskiy, much less talk about Russia-Ukraine cooperation, since the election results were not yet official.
The leaders of the United States, the European Union, Germany and France have phoned Mr Zelenskiy to give their congratulations.
Moscow “respects the choice of the Ukrainian people” and will wait for concrete steps by the new Ukrainian leader before making judgments, Mr Peskov said.
Russian prime minister Dmitry Medvedev posted on his Facebook page the election results in Ukraine showed “there is a chance to improve the relations with our country after all”.
Mr Medvedev, whose government has been supplying the Ukrainian separatists with weapons and manpower, expressed hope Mr Zelenskiy would be “pragmatic and responsible” in his approach to the conflict in the east.