The exit poll for Sunday's election, conducted by three respected Ukrainian survey agencies, found the 48-year-old candy tycoon Poroshenko getting 55.9 percent of the vote.
At a distant second was former prime minister Yulia Tymoshenko with 12.9 percent, the poll showed. Full results are expected Monday in the election that could be a critical step toward resolving Ukraine's protracted crisis.
"The country has got a new president," a confident and composed Poroshenko told several hundred journalists at his election headquarters. "I would like to thank everyone for the support that the Ukraine has showed today for me and my team."
The tycoon pledged that his first steps as president will be "to put an end to war, chaos, crime and to bring peace to the Ukrainian land." He also said his first visit would be to Donbass, Ukraine's eastern industrial region.
Poroshenko ducked the question whether he was prepared to work with Russian President Vladimir Putin but said Kiev would like to negotiate a new security treaty with Moscow.
The exit poll, which surveyed 17,000 voters at 400 precincts, claimed a margin of error of 2 percentage points, indicating Poroshenko passed the 50-percent mark needed to win without a runoff. It was conducted by the Razumkov Center, Kiev International Sociology Institute and the Democratic Initiatives Foundation.
"I would like to congratulate Ukraine with the fact that despite the current aggression by the Kremlin and the desire to break this voting, the election happened and was democratic and fair," Tymoshenko said after the polls closed. "I think this is the evidence of the strength of our nation."
The election came three months after the country's pro-Russia leader fled in February, chased from power by months of protests over corruption and his rejection of a pact with the European Union in favor of closer ties with Moscow. It also came two months after Russia annexed Ukraine's strategic Black Sea peninsula of Crimea.
Yet the question of who was able to vote Sunday loomed large over the democratic process. Some 35.5 million Ukrainians were eligible to vote, but separatists in the eastern Donetsk and Luhansk regions which have 5.1 million voters said they will not hold the vote because they are no longer part of Ukraine.
The turnout at 3 p.m. was 40 percent, according to the Election Commission.
Little voting was taking place in the east, however. The regional administration in Donetsk said only 426 of 2,430 polling stations in the region were open Sunday, and none in the city of Donetsk, which has 1 million people. There was no voting in the city of Luhansk either, but some stations were open in the wider Luhansk region.
Fighting broke out Sunday in the Luhansk town of Novoaidar, where an AP reporter heard heavy gunfire.
Sergei Melnichuk, a Ukrainian army battalion commander in Novoaidar, said about 50 armed pro-Russia rebels attacked a polling station trying to seize ballots but government forces thwarted the move and captured 13 rebels. The Interfax-Ukraine news agency quoted the deputy interior minister as saying one person was killed and another injured in the fighting.
Putin has promised to "respect the choice of the Ukrainian people" and said he would work with the winner, in an apparent bid to ease Russia's worst crisis with the West since the Cold War and avoid a new round of Western sanctions.
Many voters appreciate Poroshenko's pragmatism and his apparent knack for compromise, a unique trait in a political environment dominated by intransigent figures. Poroshenko strongly backs closer ties with the 28-nation EU, but also speaks about the need to normalize ties with Russia.
"He is a very smart man who can work hard compared to others, and he is also a businessman and knows that compromises are necessary even if unpleasant," said 55-year old Kiev teacher Larisa Kirichenko.
The interim Kiev government and the West have accused Russia of backing the separatist uprising. Moscow has denied the accusations but annexed Crimea after a separatist vote there.
Ukraine and the rest of the world have not accepted Moscow's annexation of Crimea, so residents there were allowed to travel to other areas in Ukraine to vote. It was not clear how many did so.
Ukrainian election officials said they have received as little as 26 percent of the election registers for the Donetsk region and 16 percent for the Luhansk region. Ukraine's deputy interior minister, Serhiy Yarovyi, said police could only ensure security at polling stations in just nine of the 34 electoral districts in the east.
There were plenty of disruptions Sunday in Donetsk. A rebel convoy of an armored personnel carrier and seven trucks carrying several hundred heavily armed men drove through the city, stood to attention and shot guns into the air in jubilation as several thousand supporters cheered them.
Another team of insurgents visited polling stations Sunday in Donetsk to make sure they were closed.
Outside the Donetsk administration building, which has been occupied by rebels since early April, a group of masked men drove up carrying confiscated ballot boxes and made a show of smashing them in front of news cameras.
One polling station in Donetsk opened but minutes later gunmen arrived and forced its election commission out. Gunmen also stormed the Donetsk village council in Artemivka and set the polling station ablaze, the Ukrainian Interior Ministry said.
Yet some parts of the Donetsk region remain under greater government control so voting could take place.
In the Azov Sea port of Mariupol, 202 out of the city's 216 polling stations were working. A week ago, Rinat Akhmetov, the billionaire metals tycoon who is Ukraine's richest man, had his factory workers there join police to patrol the city and evict the pro-Russia insurgents from government buildings.
"I want order in this country. We can't continue without a president. We need order," voter Gennadiy Menshykov said in Mariupol.
In the town of Krasnoarmeisk, in the western Donetsk region, a trickle of people came to cast ballots.
Ivan Sukhostatov, 37, said he had voted for peace.
"We came to show that this whole situation is contrived," he said. "One side are called terrorists, the others get called fascists. But we have no differences between us. We have one faith, we speak one language. We just want there to be peace."
Leonard reported from Donetsk, Ukraine. Nebi Qena in Novoaidar, Alexander Zemlianichenko in Slovyansk, Dmitry Kozlov in Mariupol, Ed Brown in Krasnoarmeisk and Nataliya Vasilyeva in Kiev contributed to this report.