The 48-year-old tycoon took the oath before parliament, buoyed by western support but facing a crisis in relations with Russia as a separatist uprising seethes in the east.
Russia annexed the Crimea in March, after pro-Moscow predecessor Viktor Yanukovich fled amid street protests.
“Citizens of Ukraine will never enjoy the beauty of peace unless we settle our relations with Russia. Russia occupied Crimea, which was, is, and will be, Ukrainian soil,” Poroshenko said to a standing ovation. He said he delivered that message to Russian president Vladimir Putin when they met on Friday at a Second World War commemoration in France.
Russia’s policy on Crimea remains unchanged but a Russian news agency reported Putin had ordered border security with Ukraine to be tightened, a move hailed as potentially significant since the West has pressed him to stop a flow of arms and fighters into eastern Ukraine.
Russia denies it is backing the uprising but journalists have encountered Russian nationals in separatist ranks.
Poroshenko, who earned his fortune as a confectionery entrepreneur and is known as the Chocolate King, said he intended to sign the economic part of an association deal with the European Union as a step towards full membership.
Moscow wants to keep Ukraine in its own post-Soviet sphere of influence.
In an emotional speech, Poroshenko stressed the need for a united Ukraine and the importance of ending the conflict that threatens to split the country of 45 million people.
He said it would not become a looser federalised state, as advocated by Russia.
“There can be no trade-off about Crimea and about the European choice and about the governmental system. All other things can be negotiated and discussed at the negotiation table. Any attempts at internal or external enslavement of Ukraine will meet with resolute resistance,” he said.
Since his election, government forces have stepped up operations against the separatists who want to split from Kiev and join Russia. The rebels have fought back, turning parts of the Russian-speaking east into a war-zone. Poroshenko offered to provide a safe corridor for Russian fighters to go home.
“Please, lay down the guns and I guarantee immunity to all those who don’t have bloodshed on their hands,” he said.
Switching from Ukrainian into Russian, he promised to visit the east with guarantees of Russian-language rights and proposals for decentralisation that would give its regions a bigger say in running their own affairs.
Rebel spokesmen snubbed his appeals. “What they [Kiev’s leaders] really want is one-sided disarmament and for us to surrender. That will never happen in the Donetsk People’s Republic,” said Fyodor Berezin, a separatist leader.
“As long as Ukrainian troops are on our soil, I can see all Poroshenko wants is subjugation. The fight will continue.”
Poroshenko won a landslide election on 25 May after promising to bridge the east-west divide that has split Ukraine.
Many Ukrainians hope the election of the former government minister, who is married with four children, will end the most tumultuous period in their post-Soviet history.
More than 100 people were shot dead by police in Kiev in the street protests that toppled Yanukovich. In the east, scores of people have been killed since April. The uprising is not the only challenge facing Poroshenko, who inherits a country on the verge of bankruptcy and rated one of the most corrupt and ill-governed in Europe.
Kiev is also at odds with Moscow over Russian gas. Russia is threatening to cut supplies as early as this week unless Ukraine settles its debt.
Poroshenko’s swearing-in was attended by Lithuanian president Dalia Grybauskaite, US vice-president Joe Biden and senior EU officials.
Cheering crowds later greeted him as he strolled in front of Kiev’s St Sophia’s Cathedral.
Russia’s foreign ministry did not comment on his speech, calling instead for the release of two Russian journalists detained in Ukraine. But reaction was hostile in eastern Ukraine, where government forces shelled rebels in Slovyansk and manned checkpoints on roads into the city.
In another eastern city, Luhansk, separatist leader Valery Bolotov rejected Poroshenko and Ukrainian rule. “Today Ukraine got a new president and now the blood of our people and of Ukrainians will lie on his conscience”, he said.