Viktor Yushchenko has taken the oath of office as Ukraine's new president, ending a bruising election marathon.
Forever our blue and yellow flag will fly, the president told crowds
Mr Yushchenko then addressed hundreds of thousands of supporters in Kiev's Independence Square.
The president, who has pledged to move closer to the West, told the crowd: "Our way to the future is the way of a united Europe."
Mr Yushchenko beat Moscow-backed Viktor Yanukovych in a re-run of November's disputed poll.
The 26 December repeat run-off was held after the Supreme Court ruled that the original vote - officially won by Mr Yanukovych - had been rigged.
Independent election observers said the re-run had been much fairer than earlier rounds.
At Sunday's inauguration ceremony, Mr Yushchenko stood hand on heart as the national anthem was played.
In taking the presidential oath of office, he said he would defend the unity of Ukraine.
The swearing-in was watched by eight heads of state, along with US Secretary of State Colin Powell.
Hundreds of thousands gather in Independence Square on Sunday
After meeting Mr Yushchenko, Mr Powell said: "I want to assure you that you will continue to enjoy the full support of the American government and the American people."
Russia, which had backed Mr Yanukovych, was represented only by the head of the upper house of its parliament, Sergei Mironov.
The date for the inauguration was set only this week after the Supreme Court dismissed a final appeal by Mr Yanukovych against the result.
The gathering in Independence Square allowed Mr Yushchenko to thank those who took part in what has been called the Orange Revolution - after the colour of Mr Yushchenko's camp.
The president told the massive crowd: "This is a victory of freedom over tyranny. The victory of law over lawlessness."
He added: "We are not on the outskirts of Europe, we are at the centre of Europe... Forever our blue and yellow flag will fly."
The bitterly fought election exposed deep splits between south-eastern regions, where support is high for Mr Yanukovych, and western and central Ukraine which largely backs Mr Yushchenko.
Viktor Yanukovych kept challenging the election result
On the eve of his inauguration, Mr Yushchenko urged Ukrainians to overcome divisions.
He was speaking at a ceremony on Saturday marking Ukraine's Unity Day.
Mr Yushchenko also took the symbolic oath of hetman, or leader of Cossacks - the historic defenders of Ukraine against foreign oppression.
"I am convinced that... our forefathers were also dreaming of seeing a democratic Ukraine with free people," Mr Yushchenko said in front of a crowd of some 200 Cossacks.
The day after Sunday's inauguration, Mr Yushchenko is due to meet Russian President Vladimir Putin in Moscow in what will be his first foreign visit.
Later in the week, Mr Yushchenko will also embark on a series of visits to Europe.