"Crimea was, is, and will be Ukrainian," he said in an emotional address after his swearing-in. He was greeted with a standing ovation.
"I put that clearly to the Russian leader in Normandy," he added, referring to his meeting with President Vladimir Putin at D-Day commemorations yesterday.
He stressed the unity of Ukraine, which is fighting a pro-Russian separatist uprising in the east, and said it would not become a federalised state as advocated by Moscow.
Mr Poroshenko also 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.
"I am assuming the presidency in order to preserve and strengthen Ukraine's unity," Mr Poroshenko said in an address that alternated between Ukrainian and Russian.
He promised the residents of the Donbass region, which is largely in rebel hands, that he would decentralise power and guarantee the free use of the Russian language.
He pledged to protect Ukraine's sovereignty and independence and safeguard the rights and freedoms of its citizens.
Mr Poroshenko's election came three months after his predecessor Viktor Yanukovych was toppled by street protests and fled to Russia.
Later today, he is expected to lay out a programme for restoring stability in the rebellious east and moving Ukraine into the European mainstream.
He has received messages of support from the West but is still seeking a strategy to deal with Russia's Vladimir Putin, who opposes Kiev's military drive against pro-Russian separatists.
Mr Poroshenko has promised to bridge the east-west divide that has split the country and thrust it into a battle for its very survival.
Western governments and Russia, locked in a geopolitical fight over Ukraine's future, will be watching for clues on how he intends to handle the eastern rebellions.
Mr Poroshenko says he wants closer relations with Europe.
Mr Putin has said he welcomed Mr Poroshenko's plans to stop the bloodshed, but said Ukraine must stop its "punitive" military operation.
Russia rejects charges by Kiev and the West that it is actively supporting the rebels in the Russian-speaking east.
The fighting since Mr Poroshenko's election has revealed that many of the rebels are from Russia, with dozens of dead bodies of fighters sent back across the frontier.
In a small sign of a thaw, Moscow sent its ambassador, who was withdrawn after pro-Russian President Viktor Yanukovych was toppled in February, back to Kiev to attend the swearing in.
Moscow has also begun withdrawing some of the tens of thousands of troops it had massed on the frontier.