Russia, which has been threatened with a new round of Western sanctions if it meddled further in Ukraine after its seizure of Crimea in March, said however it was willing to work with the new leaders.
"We are ready for pragmatic dialogue, on an equal footing, based on respect for all agreements, in particular in the commercial, economic and gas spheres," Foreign Minister Sergei Lavrov said in Russia's first reaction.
"As the president (Vladimir Putin) has said, we respect the result of the choice of the Ukrainian people."
Rebels have rejected dialogue with Poroshenko, with Donetsk separatist leader Denis Pushilin saying talks were only possible if Russia mediated and calling for a prisoner swap and a withdrawal of Kiev's troops.
But despite their efforts to thwart the vote, observers with the Organisation for Cooperation and Security in Europe said the election "largely upheld democratic commitments" and provided the new leader with legitimacy despite the problems in the east.
While turnout was strong across the capital Kiev and the more pro-European west on Sunday, voting was largely blocked in Donetsk and Lugansk, two regions that make up 15 percent of the electorate.
The election commission said voting had been suspended by militants in 24 of Ukraine's 213 constituencies.
"The people of Kiev who have been killing innocent civilians in the south and east, who cares who they choose as president," Donetsk resident Galina said as she handed out newspapers near a regional adminstration building now overrun by rebels.
But US President Barack Obama praised "courageous Ukrainians" for voting in the face of the militant threat.
The ballot was called after Kremlin-allied president Viktor Yanukovych -- his corruption-stained regime long a source of discontent -- was ousted in February in the bloody climax of months of protests sparked by his rejection of a historic EU pact.
Putin responded by seizing Crimea and threatening to invade the rest of Ukraine to "protect" the country's ethnic Russian community, raising the prospect of all out war on Europe's doorstep.
But Russia said last week it had started withdrawing from Ukraine's border around 40,000 soldiers whose presence had raised deep Western suspicions and prompted NATO to send additional fighters to former Soviet satellite states.
In addition to the political and security challenges ahead, Poroshenko will have to adopt painful austerity measures that world lenders are demanding in return for $27 billion (20 billion euros) in aid to prevent bankruptcy.
He will also have to negotiate with Russia over key gas supplies after the Kremlin said it would cut shipments by early June if Kiev does not pay a bill.