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.