• Zelensky challenged incumbent president Petro Poroshenko.
• Poroshenko has admitted defeat but told supporters gathered in Kiev that he will not leave politics.
Ukrainian comedian Volodymyr Zelensky has won a run-off election to become the country's next president by a landslide, exit polls suggest.
The polls give him more than 70% support. He dominated the first round of voting three weeks ago when 39 candidates were on the ticket.
Mr Zelensky challenged incumbent president Petro Poroshenko.
Mr Poroshenko has admitted defeat but told supporters gathered in Kiev that he will not leave politics.
"I will never let you down," Mr Zelensky told supporters on Sunday.
He added: "While I am not formally president yet, as a citizen of Ukraine I can tell all post-Soviet countries: 'Look at us! Everything is possible!'"
If polls are correct, he will be elected for a five-year term.
Ukraine's president holds significant powers over the security, defence and foreign policy of the country.
Humiliation for Poroshenko
Analysis by Jonah Fisher, BBC News, Kiev
Ukraine's choice was between an experienced politician with five years as president on his CV and a comedian wielding little more than a blank sheet of paper. That so many people have opted for Volodymyr Zelensky is a humiliation for Petro Poroshenko.
Thirty-seven candidates were removed from the ballot paper from the first round and yet the president only picked up about 9% more votes this time. Mr Zelensky gained almost 45 percent.
This feels like a massive protest vote and for now Mr Zelensky and his campaign team are celebrating.
It's hard to see the feeling lasting long. The hard work will come when they have to start fleshing out what are at the moment vague policies.
It's one thing to have bold ideas but quite another to implement them.
Polls gave Mr Poroshenko, who has been in power since 2014, 25% of the vote.
The billionaire was elected after an uprising overthrew the country's previous, pro-Russian government.
"The outcome of the election leaves us with uncertainty [and] unpredictability," he said after exit polls were released.
"I will leave office but I want to firmly stress - I will not quit politics," he added.
Mr Zelensky, 41, is best known for starring in a political satirical drama called Servant of the People in which his character accidentally becomes Ukrainian president.
He ran under a political party with the same name as his show.
With no previous political experience, his campaign focused on his difference to the other candidates rather than on any concrete policy ideas.
Despite this, he won the first round with more than 30% of the vote - almost double what Mr Poroshenko got when he finished in second place with 15.95%.