Yushchenko won 54.08% of the vote compared to 42.13% for pro-Russian Prime Minister Viktor Yanukovich, based on reporting from 90.03% of the country's precincts.
Earlier, Yushchenko had claimed victory in the historic presidential election re-run.
He told his supporters on Monday morning that the vote was a triumph for the country and proclaimed that "now we are free" from dominance by neighbouring Russia.
Speaking in a hall at his campaign headquarters, the man who led the "orange revolution" that shook Ukraine for weeks said: "It has happened. For 14 years we have been independent, but now we are free.
"This is a victory for the Ukrainian people, for the Ukrainian nation."
Three independent exit polls published at the close of voting on Sunday gave Yushchenko at least a 15-point lead over his rival.
"It has happened. For 14 years we have been independent, but now we are free. This is a victory for the Ukrainian people, for the Ukrainian nation"
Ukraine presidential candidate
A Yushchenko win would mark a dramatic political turnaround in a country where only last month state broadcast media all but banished him from the airwaves, and Russian President Vladimir Putin publicly backed Yanukovich.
The 54-year-old Yanukovich was officially declared winner of a 21 November presidential ballot and was twice congratulated by Putin, but Yushchenko supporters protested against the result, which was later judged fraudulent and thrown out by the Supreme Court.
"Today we are turning the page on human disrespect, censorship, lies and violence," Yushchenko said.
"People who were dragging the country towards the abyss are today stepping into the past."
After speaking at his campaign headquarters, Yushchenko returned to Kiev's central Independence Square where he told tens of thousands of cheering supporters, many waving orange flags, that "an independent and free Ukraine now lies before us".
However, he repeated his call for his supporters to remain in the square until he is officially confirmed as the winner of the election.
Yushchenko supporters are
already celebrating victory
Earlier, Yanukovich held a press conference where he stopped short of conceding defeat, but promised to fight in a new opposition should his rival assume the presidency.
"I expect to win, but if I am defeated then a strong opposition will be created, it will be in the parliament" and Yushchenko "will learn what an opposition really is", the 54-year-old Yanukovich vowed.
Yushchenko, whose support is strongest in the agrarian, nationalist, Ukrainian-speaking west of the country, has pledged to lead the nation towards eventual membership in the European Union and the North Atlantic Treaty Organisation.
Yanukovich, whose base is in the industrialised, Russian-speaking east, pledged to preserve and fortify traditional ties with Russia, and thus enjoyed backing from Moscow.
Apart from the east-west split within Ukraine itself, the battle to succeed President Leonid Kuchma has also enflamed tensions between Western countries seeking to broaden their influence and Russia which has bridled at what it sees as encroachment into its strategic backyard.
The United States, which has rejected accusations from Yanukovich and Russia that it financed Yushchenko's campaign, warned Ukrainian authorities after the voting ended to make sure the count was honest.
"I expect to win, but if I am defeated then a strong opposition will be created, it will be in the parliament [and Yushchenko] will learn what an opposition really is"
Ukraine presidential candidate
"We hope for a free, fair vote that meets international standards and results in an outcome truly reflecting the will of Ukraine's people," a US Department of State spokesman said in Washington.
Apart from the national and international tensions it has generated, the Ukrainian election campaign was marked by a dioxin poisoning episode that took Yushchenko off the campaign in September with a severe illness that has left his face sallow, puffy and pock-marked.
Yushchenko has insisted it was an attempt to murder him. He fell ill the day after having dinner with the chief of Ukraine's SBU intelligence service, Ihor Smeshko, who has denied that he or his agency had any role in the poisoning.
Throughout the evening after polls closed, Kiev's Independence Square, the locus of dramatic protests following the contested 21 November election, was again the centre of a raucous and jubilant pro-Yushchenko street party.
About 12,500 observers from dozens of international and domestic institutions, and a number of foreign governments were registered to monitor the voting, compared to the 5000 who observed the previous runoff vote.
Violence that some feared could occur between the bitterly divided supporters of the two camps failed to materialise by late Sunday, and the country's interior ministry reported shortly before polls closed that the election had been carried out with no unusual incidents.