In Georgia, President Mikhail Saakashvili — who came to power a year ago in a people power movement known as the Rose Revolution — displayed his enthusiasm through sartorial symbolism: He wore an orange tie in honor of Yushchenko's campaign color.
"Everybody has seen the color of the tie I've worn for the past few days," he said. "My preferences are obvious."
Saakashvili, who studied law in then-Soviet Ukraine and speaks some Ukrainian, has been a vocal supporter of the Ukrainian opposition. "I'm very happy today," he said. "It's a historic day."
In Poland, whose pro-democracy icon Lech Walesa recently traveled to Kiev to deliver a stirring message of solidarity with Yushchenko, President Aleksander Kwasniewski gushed with enthusiasm.
"I share the joy of the Ukrainians rejoicing now in the streets," said Polish President Aleksander Kwasniewski, who has helped mediate in the crisis. "I am also happy because we managed to solve the Ukrainian crisis through legal means."
Poland, which shares a border with Ukraine, has been nervously awaiting the outcome of the electoral crisis, which will likely determine whether Ukraine moves closer to the West as Poland has done, or falls more deeply under the influence of Russia.
Thursday's Supreme Court ruling, made after five days of hearings by the court's 21 justices, was a huge blow to Russian President Vladimir Putin and outgoing Ukrainian President Leonid Kuchma, who had openly backed the government candidate, Prime Minister Viktor Yanukovych.
Away from the jubilant celebrations in Kiev, the mood in rural Ukraine is very different, reports CBS News Correspondent Sheila MacVicar. On the streets in smaller cities, people say they're afraid of instability, chaos and even that their country might break up.
"I'm not thinking about either candidate ... I'm worried about my country," one Ukrainian man said.
The opposition had pinned its hopes on the court in its bid to overturn the results of the Nov. 21 run-off vote, in which Yanukovych was declared the winner. The opposition said the vote was rigged to cheat Yushchenko of victory.
In Washington, White House spokesman Scott McClellan called the court's decision "an important step in moving toward a peaceful, democratic resolution that reflects the will of the people."
U.S. State Department spokesman Richard Boucher said American officials "certainly agree with the decision that the results that the last round was marked by significant fraud and that it therefore can't be upheld as a fair result."
"What is important now is to move ahead quickly, as called for by the Supreme Court, to ensure a new vote that is fair, free and that results in an outcome that reflects the will of the Ukrainian people," Boucher said.
Britain's Foreign Office also welcomed the ruling.
"It's an important sign that proper legal and democratic institutions are functioning in accordance with the law," the department said. "It is important that there is a free and fair election and that the result reflects the will of the Ukrainian people."
Putin was in India and made no public comment on the Supreme Court verdict. He had sharply derided the idea of holding a new runoff.
Fyodor Lukyanov, editor of a leading Russian foreign policy journal, said that no matter who becomes president, Russia has suffered "its biggest foreign policy defeat since the collapse of the Soviet Union" and Ukraine has been pushed closer to the West.
Grigory Yavlinsky, a liberal Russian political leader, also said the ruling had great significance.
"For the first time in a post-Soviet country, falsifications, the use of administrative resources and dishonoring people's will were rebuffed at the highest judicial level," he said.
But Sergei Markov, a pro-Kremlin analyst, said the decision was illegal and meant Kuchma had capitulated under pressure from anti-Russian "radicals" in Yushchenko's camp who he said "shake when they hear the word Russia."
Yushchenko supporters who put up a tent outside the Ukrainian Embassy in Warsaw a week ago were thrilled.
"Without this decision, change would not have been possible" in Ukraine, said Krzysztof Swiernalis, a Polish businessman whose wife is Ukrainian. "Maybe we would have had to wait another 20 years. This is a great chance for Ukraine to follow its own road."