Exit polls suggest confectionery magnate Petro Poroshenko has won Ukraine's presidential election with an absolute majority.
That would avert the need for a runoff vote next month that Mr Proshenko had warned could destabilise the country.
Two polls gave Mr Poroshenko, a billionaire businessman known as the 'Chocolate King', with long experience in government, 55.9-57.3%, well ahead of former prime minister Yulia Tymoshenko in second place with just over 12%.
If confirmed by results tomorrow, there will be no need for a runoff vote on 15 June.
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 Mr Poroshenko, armed pro-Russian separatists barred people from voting in much of Ukraine's Donbass industrial heartland today, turning the main city of Donetsk into a ghost town.
Mr 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 neighbour, which provides most of its natural gas and is the major market for its exports.
Today's election marked the culmination of a revolution that erupted last November, forced a pro-Russian president to flee in February and spiralled into an existential crisis when Russia 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 Yanukovych.
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.
Mr Putin, who branded eastern Ukraine "New Russia" last month, has made more accommodating noises of late, saying yesterday 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% of the potential electorate from the election could give Russia an excuse to raise doubts about the victor's legitimacy and continue applying pressure on the new president in Kiev.
Mr Poroshenko is not a new face in Ukrainian politics, having served in a cabinet under Mr Yanukovych and also under a previous government led by Mr Yanukovych's rivals.
This breadth of experience has given him a reputation as a pragmatist capable of bridging Ukraine's divide between supporters and enemies of Russia.
He nevertheless was a strong backer of the street protests that toppled Mr Yanukovych 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.
In a statement, US President Barack Obama did not pre-empt the results by naming Mr Poroshenko but he praised Ukrainians for turning out to vote despite violence and said the United States looked forward to working with Ukraine's new president.
Italian journalist killed in shell attack
Meanwhile, an Italian journalist has been killed during a mortar shell attack close to Slaviansk, eastern Ukraine, Rome's foreign ministry announced.
"Unfortunately, all of the information points to the fact that he has died," a spokeswoman said.
The exact circumstances surrounding his death were still unclear, added the ministry, saying the situation was "difficult to verify" even for the Ukrainian authorities.
The journalist was named by Italian media as Andrea Rocchelli, 30, a founder of the photo agency Cesura.
His body had been taken to a hospital close to Slaviansk for identification, the ministry said.