Sunday’s election has about 35 million eligible voters, but several million in Russian-annexed Crimea and rebel-held parts of eastern Ukraine are either unable or unwilling to cast their ballots.
The polling stations will close at 8pm (1700 GMT). An early count is expected overnight on Monday.
The opinion polls predict a humiliating defeat for Poroshenko, who came to power five years ago with 55 percent support after a deadly pro-West uprising removed his Russia-backed predecessor Viktor Yanukovich in 2014.
He has been projecting himself as Ukraine’s passionate commander-in-chief since the so-called Revolution of Dignity resulted in the war between Moscow-backed separatists in Donetsk and Luhansk regions, and the Ukrainian army. The conflict has killed more than 13,000 people.
During the election campaign, Poroshenko told Ukrainians that Zelensky would fail to protect them from Russia’s President Vladimir Putin.
But the majority of the population holds the incumbent responsible for the government’s failure to tackle endemic corruption and the deteriorating living conditions.
More than 72 percent of voters are expected to support the comic, who has been playing a corruption-busting president on TV for the last three years.
In the first round of vote held on March 31, Zelensky came first among 39 presidential candidates with more than 30 percent of ballots – double of what Poroshenko secured.
The comic benefited from the support of Ukrainians seemingly tired of mainstream politicians.
Zelensky’s supporters, who spoke to Al Jazeera during the first round of voting said they were backing him because he was not a politician.
The millionaire of Jewish descent especially appeals to young people and the Russian-speaking population.
The father of two from the industrial city of Krivy Rig in central Ukraine has shunned campaign rallies in favor of comedy shows, and prefers to get his message across through YouTube clips and social media updates.
Many people also fear if Zelensky becomes president, the country will be run from the shadows by self-exiled oligarch Ihor Kolomoisky.
Kolomoisky, who has been living in Israel since Ukraine started investigating alleged financial wrongdoings in his now-nationalized PrivatBank, owns the television channel that airs Zelensky’s shows.
