Liberal opposition leader Viktor Yushchenko will be sworn in as Ukrainian president on Sunday after weeks of political turmoil.
Viktor Yushchenko drew vast crowds into central Kiev
The date was set by Ukraine's parliament soon after the Supreme Court confirmed Mr Yushchenko's victory.
The court dismissed a final appeal by former Prime Minister Viktor Yanukovych who had challenged the re-run poll.
Russian President Vladimir Putin, who had shown support for Mr Yanukovych, sent congratulations to Mr Yushchenko.
"The development of neighbourly and equal relations with Ukraine is one of Russia's most important national priorities," Mr Putin is reported to have written to Mr Yushchenko.
Independent election observers said the re-run elections on 26 December had been much fairer than the earlier rounds.
The re-run was held after Mr Yushchenko's supporters staged massive protests over the outcome of a November poll, alleging vote-rigging by Mr Yanukovych.
Viktor Yanukovych kept challenging the election result
Deliberations at the Supreme Court continued until 0230 (0030 GMT) on Thursday, when chief presiding justice Anatoly Yarema announced that the court was to uphold Mr Yushchenko's election victory.
"The decision is final and cannot be appealed," Mr Yarema said.
The announcement came after Ukraine's newspapers printed early editions carrying official results of the election, in which Mr Yushchenko beat his rival by eight percentage points.
Mr Yushchenko's victory celebrations had been put on hold by dogged appeals from his rival, who alleged widespread vote-rigging and electoral fraud.
Supporters who remained in the city awaiting the court's decision were jubilant at the judgement.