The polls give the political newcomer, who dominated the first round of voting three weeks ago, more than 70% support.
Mr Zelensky, 41, challenged incumbent president Petro Poroshenko who has admitted defeat.
The apparent result is being seen as a huge blow to Mr Poroshenko and a rejection of Ukraine's establishment.
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| Ukrainian presidential candidate Volodymyr Zelenskiy reacts following the announcement of the first exit poll in a presidential election at his campaign headquarters in Kiev, Ukraine. |
"I will never let you down," Mr Zelensky told celebrating supporters on Sunday.
"I'm not yet officially the president," he added. "But as a citizen of Ukraine I can say to all countries in the post-Soviet Union: Look at us. Anything is possible!"
If polls are correct, he will be elected for a five-year term. Official results are expected to come in throughout Sunday night.
Mr Zelensky is best known for starring in a satirical television series in which his character accidentally becomes Ukrainian president.
The president holds significant powers over the security, defence and foreign policy of the country.
Mr Zelensky starred in the long-running satirical drama Servant of the People in which his character accidentally becomes Ukraine's president.
He plays a teacher who is elected after his expletive-laden rant about corruption goes viral on social media.
He ran under a political party with the same name as his show.
Analysts believe Mr Zelensky's informal style and vow to clean up Ukrainian politics resonated with voters who are disillusioned with the country's path under Mr Poroshenko.
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| Ukrainian President Petro Poroshenko (left) and Ukrainian presidential candidate and popular comedian Volodymyr Zelenskiy (right) argue their debates at the Olympic stadium in Kiev, Ukraine, on Friday. |
Eschewing traditional campaign tactics, Mr Zelensky channelled his on-screen persona by promising to stamp out corruption and loosen the grip of oligarchs on Ukraine.
Experts say his supporters, frustrated with establishment politicians and cronyism, have been energised by his charisma and anti-corruption message.
His critics, meanwhile, are sceptical about his credentials, with many expressing concern over his close links to the billionaire oligarch Ihor Kolomoyskyi.
They have expressed doubts that he will be able to take on the country's influential oligarchs and stand up to Russian President Vladimir Putin.
