After several hours of deliberations, Judge Olexander Nechitailo announced the court's decision to "leave the lawsuit by presidential candidate Yulia Tymoshenko without consideration".
On Friday, Tymoshenko presented nine volumes of evidence and appealed for the court to declare the election void, claiming Yanukovych had only managed to beat her to the presidency through fraud.
Hundreds of her supporters gathered outside the court that day, but they were dwarfed by a much larger pro-Yanukovych crowd.
Despite the prime minister's allegations, observers said the presidential vote was fair and democratic and most analysts agree Tymoshenko had been facing an uphill struggle to have the election overturned.
Yanukovych defeated Tymoshenko by just 3.5 per cent of the vote, under 890,000 ballots, according to the final official results.
He has denied the allegations of vote-rigging and is due to be sworn into office on February 25.
A Yanukovych party official called Tymoshenko's decision "fairly predictable".
"The lack of proof forced Tymoshenko to admit the obvious fact - that Viktor Yanukovych won the election," Anna German, the vice-chairwoman of the Party of Regions, said.
Ukraine's parliament, where Yanukovych's Regions Party makes up the largest bloc, has launched an official motion to throw out Tymoshenko and her government.
Yanukovych was denied the presidency in 2004 when a wave of protests against electoral fraud developed into the Orange Revolution and ended with Viktor Yushchenko being elected as president.
After Tymoshenko's climbdown on Saturday, Yanukovych's is likely to be sworn in on February 25 as previously planned.