His surge in popularity is a rebuke to Ukraine's political elite, who have struggled to revive the economy and put an end to a conflict with Russian-backed separatists in the country's east.
Critics fear that a Zelensky presidency could throw the country into chaos, but the comedian has promised to surround himself with able advisors and on Thursday was set to reveal his "dream team".
Anticipation was also building ahead of a presidential debate due on Friday, the first and only one of the presidential campaign.
The two candidates confirmed on Wednesday they would take part in the debate in a sports arena that seats 70,000 people.
Zelensky's spokeswoman Iryna Pobedonostseva said he was looking forward to facing off with his rival.
"Preparations for the debate are in full swing. You will see the results tomorrow," she told AFP.
Zelensky suggested he would have an easy time in the debate given Poroshenko's record.
"I don't want to call anyone names, insult anyone or engage in mud-slinging," he told local media.
"After what has been done over the last five years I believe I can simply keep mum."
Poroshenko, who took power in 2014 after a popular uprising ousted a Kremlin-backed leader, has asked Ukrainian voters to give him a second chance.
Supporters credit Poroshenko, 53, with rebuilding the army, securing an Orthodox Church independent of Russia and winning visa-free travel to Europe.
'Everyone has gone mad'
He has said he needs more time to push through economic reforms and that a political neophyte at the helm of Ukraine would be Moscow's dream come true.
Poroshenko has sought to cast himself as the only Ukrainian politician who can take on Russian President Vladimir Putin and settle the war with separatists in the east, a conflict that has claimed some 13,000 lives.
Former prime minister Yulia Tymoshenko, who was knocked out in the first round of voting last month, said it was time to accept a new political reality.
"Mathematics already tells us that Volodymyr Zelensky will win the second round," she said in a video address on Wednesday.
"This is objective reality. It's time to think of how to live with this," she said, calling for calm and unity.
The latest survey published on Thursday gave Zelensky 73 percent of the vote and only 27 percent to Poroshenko, consistent with other recent polls.
Poroshenko has fought hard to recover lost ground in a bruising campaign after Zelensky leapfrogged the political establishment in the first round of voting on March 31.
The star of sitcom "Servant of the People" -- in which he plays a school teacher who becomes Ukrainian president -- has capitalised on widespread frustration over the economy and corruption in the country of 45 million people.
The campaign has been bitter, with the candidates trading insults on television and in social media. Both men even underwent drug tests at Zelensky's insistence.
Nerves have begun to fray in a country that went through popular uprisings in 2004 and 2014. The latest edition of magazine Novoe Vremya declared on its cover: "Everyone has gone mad."