Many voters appreciate Poroshenko's pragmatism and his apparent knack for compromise. 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.
Anastasia Fedchenko of Kiev said Poroshenko "is not the worst candidate that Ukrainians could have elected."
The question of who was able to vote loomed large over the democratic process. Separatists in the eastern Donetsk and Luhansk regions — which have 5.1 million voters — rejected the vote because they say they are no longer part of Ukraine.
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.
It was also not clear if voters from Crimea were able to travel to other areas in Ukraine to vote.
There were plenty of disruptions Sunday in Donetsk. A rebel convoy carrying several hundred heavily armed men drove through the city Sunday, then climbed out, stood to attention and shot their guns into the air as several thousand supporters cheered.
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.
Another team of insurgents visited polling stations in Donetsk to make sure they were closed. One polling station in the city opened but minutes later gunmen arrived and forced its election commission out. Gunmen also stormed the village council in Artemivka and set that polling station ablaze, the Ukrainian Interior Ministry said.
An Associated Press reporter heard heavy gunfire Sunday in Novoaidar in the Luhansk region.
Sergei Melnichuk, a commander of a pro-Ukrainian militia in Novoaidar, said about 50 armed rebels attacked a polling station trying to seize ballots, but government forces thwarted the move and captured 13 of them. The Interfax-Ukraine news agency quoted the deputy interior minister as saying one person was killed in the fighting.
Voting did take place in some parts of the Donetsk region that remain under government control.
In the Azov Sea port of Mariupol, 202 out of the city's 216 polling stations were working. Rinat Akhmetov, the billionaire metals tycoon who is Ukraine's richest man, had his factory workers there join police a week ago 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."
The Ukrainian exit polls surveyed 17,000 voters at 400 precincts and indicated Poroshenko passed the 50 percent mark needed to win without a runoff. It claimed a margin of error of 2 percentage points and was conducted by the Razumkov Center, Kiev International Sociology Institute and the Democratic Initiatives Foundation.
Leonard reported from Donetsk, Ukraine. Nebi Qena in Novoaidar, Alexander Zemlianichenko in Slovyansk, Dmitry Kozlov in Mariupol, Ed Brown in Krasnoarmeisk and Maria Danilova in Kiev contributed to this report.