Two polls gave Poroshenko, a billionaire businessman with long experience in government, 55.9 to 57.3 percent, well ahead of former prime minister Yulia Tymoshenko in second place with just over 12 percent. If confirmed by results on Monday, there will be no need for a runoff vote on June 15.
Poroshenko said there should also be a parliamentary election this year and promised he would never recognise Russia's "occupation of Crimea". Asked about relations with Russia, he said the "sovereignty and territorial integrity" of Ukraine were paramount for him.
Ukrainians, weary of six months of political turmoil, hope their new president will be able to pull their country of 45 million people back from the brink of bankruptcy, dismemberment and civil war.
But, highlighting the scale of the challenge facing Poroshenko, armed pro-Russian separatists barred people from voting in much of Ukraine's Donbass industrial heartland on Sunday, turning the main city of Donetsk into a ghost town.
Poroshenko, 48, has promised closer economic and political ties with the West in defiance of Russian President Vladimir Putin, but he will also have to try to mend shattered relations with Ukraine's giant northern neighbor, which provides most of its natural gas and is the major market for its exports.
Sunday's election marked the culmination of a revolution that erupted last November, forced a pro-Russian president to flee in February and spiraled into an existential crisis when Moscow responded by declaring its right to invade Ukraine.
The pro-Moscow separatists have proclaimed independent "people's republics" in the provinces of Donetsk and Luhansk and blocked voting there as that would imply they were still part of Ukraine. Nor was any vote held in Crimea, which Russia annexed in March after the overthrow of President Viktor Yanukovich.
Ukrainian officials hailed a high voter turnout in much of the sprawling country but said only about 20 percent of polling stations in the two restive eastern regions had functioned.
Putin, who branded eastern Ukraine "New Russia" last month, has made more accommodating noises of late, saying on Saturday he would respect the voters' will. He has announced the pullback of tens of thousands of Russian troops massed on the border.
But the absence of more than 15 percent of the potential electorate from the election could give Moscow an excuse to raise doubts about the victor's legitimacy and continue applying pressure on the new president in Kiev.
Poroshenko is hardly a new face in Ukrainian politics, having served in a cabinet under Yanukovich and also under a previous government led by Yanukovich's foes. This breadth of experience has given him a reputation as a pragmatist capable of bridging Ukraine's divide between supporters and foes of Moscow.
He nevertheless was a strong backer of the street protests that toppled Yanukovich and is thus acceptable to many in the "Maidan" movement of pro-European protesters who have kept their tented camp in the capital to keep pressure on the new leaders.
Since Yanukovich fled in February after more than 100 people were killed, Moscow has refused to recognize the interim leaders in Kiev, describing them as a fascist junta who threaten the safety of millions of Russian speakers.
Ukrainians hope the vote can help because Moscow could not so quickly dismiss an elected leader with a solid mandate.
The United States and European Union also view the election as a decisive step towards ending their worst confrontation with Moscow since the Cold War.
Their response to Russian interference in Ukraine so far has been limited to freezing the assets of a few dozen Russian individuals and small firms. But they have threatened to take far more serious measures, even targeting whole sectors of Russian industry, if Moscow interferes with the vote.
Some Ukrainians in the east who tried to vote complained about being denied their democratic right.
"What kind of polls are these? Things are bad," said pensioner Grigory Nikitayich, 72, in Donetsk.
Even Ukrainian soldiers sent to assert the government's authority in the east said they had no place to vote.
"Our superiors promised we would be able to vote here but it turns out that is not so. This is a violation of my rights, it's ridiculous - I am here to safeguard an election in which I cannot vote," said Ivan Satsuk, a soldier from the Kiev region sent to man a roadblock near the eastern port of Mariupol.
Ukraine's interim Prime Minister Arseny Yatseniuk hailed Sunday's election as a victory for democracy and the rule of law despite the disruption in the east.
"Efforts by the Russian Federation and the terrorists it finances to derail the elections are doomed to failure. We will have a legitimate head of state," he said before polls closed.
Moscow denies financing or training the separatists, denials that Western countries dismiss as absurd.
Putin pledged on Saturday to "respect" the people's choice and work with Ukraine's new administration - a conciliatory move during an economic forum at which he had acknowledged that US and EU sanctions over Ukraine were hurting the Russian economy.
He played down talk of a return to Cold War with the West and dismissed the idea he was bent on restoring the former USSR, whose collapse he has in the past lamented.