Mr Yatsenyuk’s People’s Front appeared to have performed unexpectedly well, polling in the region of 21%.
The Self Help Party, based in western Ukraine, was third with more than 13%, the exit polls indicated.
Correspondents say all three groups are strongly pro-European and should give Mr Poroshenko a strong mandate to pursue democratic reforms and a plan to end the conflict in the east.
Four other party lists seemed set to enter parliament, overcoming a 5% threshold. They include the Opposition Bloc, formed by allies of ousted Pro-Russia President Viktor Yanukovych.
Its leader Yury Boyko described the elections as the dirtiest in the country’s history.
The picture is complicated by the fact that almost half of the 450 seats are from single-member constituencies, chosen on a first-past-the-post basis.
However, 27 seats from Crimea and rebel-held areas will remain vacant.
Preliminary official results are expected on Monday.
Turnout in the election was just over 40% by 16:00 local time (14:00 GMT), the central electoral commission said, four hours before polls closed.
Earlier in the day, Mr Poroshenko briefly visited the eastern town of Kramatorsk, in an area of Donetsk region recaptured by government forces from separatist rebels.
International observers expressed “serious concerns” over the effect the violence in the east of the country is having on the election.Packers vs Saints Live Stream The head of an Organisation for Security and Cooperation in Europe (OSCE) observer mission, Swedish MP Kent Harstedt, said this was the most challenging of all the elections he had observed.
He feared it would difficult to reach out to hundreds of thousands of displaced people in eastern Ukraine, but also said he hoped the poll could be a turning point.
OSCE monitors were also present in Moscow to observe voting by the estimated two to three million Ukrainian citizens there.WWE Hell in a Cell 2014 Live Stream Mr Poroshenko later voted in the capital Kiev. “I voted for a united, indivisible, European Ukraine,” he tweeted.
Mr Yanukovych fled in February after a wave of pro-Western protests in Kiev triggered by his refusal to sign a partnership agreement with the European Union.