Tymoshenko had previously refused to concede to Yanukovych
Prime Minister Yulia Tymoshenko has dropped her legal challenge against her rival's victory in Ukraine's presidential election.
Mrs Tymoshenko said the court was not interested in giving her justice in her case against winner Viktor Yanukovych.
The Kiev court had suspended the result when Mrs Tymosheko appealed on Tuesday, claiming the poll was rigged.
International monitors deemed the vote free and fair, and Mr Yanukovych is due to be inaugurated on 25 February.
Ukrainian Central Electoral Commission's declaration on Sunday that Mr Yanukovych had won the vote by a margin of 3.48%.
Mrs Tymoshenko complained that the court proceedings were biased against her.
"Given that the court is refusing to establish the truth in essence, I withdrew my lawsuit at today's morning sitting of the Supreme Administrative Court and asked the court to stop this show, which bears no resemblance to justice," she said.
Mrs Tymoshenko had so far rejected Mr Yanukovych's appeals for her to accept defeat, claiming the election was marred by "systemic, fundamental and general falsifications".
By Dariya Merkusheva
BBC News, Kiev
Yulia Tymoshenko seems to have no other legal options left to challenge Viktor Yanukovych's victory. She has already said she cannot appeal to the supreme court.
Her party was divided in the first place on whether to pursue the legal path in challenging the elections results given the international observers opinion that these elections were as free and fair as they can get. But she insisted she had enough evidence to support her case.
Mr Yanukovych has said he will not be able to work with her as a Prime-Minister - he would like to see her as a leader of the parliamentary opposition. She has refused to step down.
Now, the parliament is set to form a new coalition which will allow MPs to vote Ms Tymoshenko out and to choose a new government, in which she will have no role to play.
The country is in a desperate economic situation - this year's budget is still not approved, and pending the political crisis is a much needed IMF loan.
As recently as Friday she had appealed for the poll to be declared void, saying: "I cannot accept double standards and I cannot give up".
The prime minister said more than a million votes, which she said were decisive to the outcome, were invalid.
But she said she would not call people on to the streets to protest, as she had done during the Orange Revolution after the 2004 presidential election.
Mr Yanukovych was pronounced the victor after that vote, only for the result to be overruled because of vote-rigging.
The uprising eventually brought Ms Tymoshenko's erstwhile ally, President Viktor Yushchenko, to power.
Ukraine has been in political deadlock for several years, undermining its ability to deal with a severe economic crisis. Analysts said Mrs Tymoshenko's challenge would only prolong the instability.
With Mrs Tymoshenko still heading the government, stalemate is likely to continue. Mr Yanukovych has said he wants to form a new coalition, and may try to call snap parliamentary elections.