The 48-year-old billionaire took the oath of office before parliament, buoyed by Western support but facing an immediate crisis in relations with Russia as a separatist uprising seethes in the east of his country.
Russia annexed the Crimean peninsula in March, weeks after street protests ousted Poroshenko's pro-Moscow predecessor, in a move that has provoked the deepest crisis in relations with the West since the Cold War.
"Citizens of Ukraine will never enjoy the beauty of peace unless we settle down our relations with Russia. Russia occupied Crimea, which was, is, and will be Ukrainian soil," Poroshenko said in a speech that was greeted with a standing ovation.
He had told this to Russia's Vladimir Putin when the two met on Friday at a World War Two anniversary ceremony in France, he said.
Poroshenko, who earned his fortune as a confectionery entrepreneur and is known locally as the "Chocolate King", said he intended very soon to sign the economic part of an association agreement with the European Union, as a first step towards full membership.
This idea is anathema to Moscow, which wants to keep Ukraine in its own post-Soviet sphere of influence.
His voice swelling with emotion, Poroshenko stressed the need for a united Ukraine and the importance of ending the conflict that threatens to further 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," Poroshenko said.
Cheering crowds later greeted him on a walkabout in blazing sunshine on the square in front of Kiev's St Sophia's Cathedral, which was decked with the blue and yellow national flag.
EASTERN WAR ZONE
Since Poroshenko's election, government forces have begun an intensified campaign against the separatist rebels in eastern Ukraine who want to split with Kiev and become part of Russia.
The rebels have fought back, turning parts of the east into a war zone. On Friday they shot down a Ukrainian army plane and killed a member of the interior ministry's special forces in the separatist stronghold of Slaviansk, where residents said shelling continued all day.
Poroshenko urged the pro-Moscow separatists to lay down their arms and said he would guarantee a safe corridor for Russian fighters to go home.
"I don't want war; I don't want revenge. I want peace and I want peace to happen," he said. "Please, lay down the guns and I guarantee immunity to all those who don't have bloodshed on their hands."
Switching to Russian from Ukrainian to address the people of the troubled east, he said they had been duped by myths about the Kiev leadership which had been stoked by Russian propaganda.
He said he would soon visit them with guarantees of Russian-language rights and proposals for de-centralisation, that would give their regions a bigger say in running their own affairs.
In the days leading up to his inauguration, Poroshenko met both U.S. President Barack Obama, who warmly endorsed his leadership, as well as Russia's Putin.
At a brief meeting in France, where they were attending World War Two commemorations, French officials said Poroshenko and Putin shook hands and agreed that detailed talks on a ceasefire between Kiev government forces and the pro-Russian separatists would begin within a few days.
Russia denounced the overthrow of pro-Moscow President Viktor Yanukovich and has accused the Ukrainian authorities of worsening the crisis in the east by resorting to military force instead of dialogue.
It denies accusations by Kiev and Western governments that it is supporting the rebels.
Putin told reporters he welcomed proposals set out by Poroshenko for ending the conflict. However he declined to say what they were and said Ukraine must halt what he called "punitive" military operations against pro-Russian separatists.
The two countries are also at odds over the pricing of Russian natural gas, with Moscow threatening to cut supplies as early as next week unless Ukraine settles its debt, the amount of which is disputed.