Mr Zelenskiy won the second round of a presidential election against incumbent Petro Poroshenko by a huge margin. The poll said he had won 73 percent of the vote versus the 25 percent won by Poroshenko. If the polls are correct, he will be elected for a five-year term.
Mr Zelenskiy dominated the first round of voting three weeks ago when 39 candidates were on the ticket.
After voting had concluded, he said: “Today it will be the victory of Ukrainians, the victory of Ukraine, and – I hope – the victory of a fair choice.”
The 41-year-old comedian is best known for staring in a political satirical drama where his character accidentally becomes the Ukrainian President.
If the exit polls prove correct, he will take over the leadership of the country on the frontline of the West’s standoff with Russia following Moscow’s annexation of Crimea.
But Mr Zelenskiy has no previous political experience and few detailed policies.
He has however promised to end the war in the eastern Donbass region and to elimitate corruption amid huge anger over rising prices and declining living standards.
But investors are worried, and want reassurances he will accelerate the various reforms needed to attract foreign investment and ensure the country remains part of the International Monetary Fund (IMF) programme.
Serhiy Fursa, an investment banker at Dragon Capital in Kiev, said: “Since there is complete uncertainty about the economic policy of the person who will become president we simply don’t know what is going to happen and that worries the financial community.
“We need to see what the first decisions are, the first appointments. We probably won’t understand how big these risks are earlier than June. Perhaps nothing will change.”
Mr Poroshenko conceded he had been soundly beaten in the run-off vote and would be leaving office next month, but said he has no plans to quit politics altogether.
The loss is a bitter blow to the incumbent, who tried to rally Ukrainians by casting himself as a bulwark against Russian aggression and a champion of Ukrainian identity.
This is a breaking story. More to follow.