The about-turn by the fiery Tymoshenko left the way clear for Yanukovich to be inaugurated as president on Feb. 25 as scheduled - though she herself still insisted he had not been legitimately elected.
The charismatic 49-year-old premier, who had alleged vote cheating by her opponent in the Feb. 7 runoff and had been pressing for a new round of voting, said she was withdrawing her legal case because the court had refused to study the evidence she had put before it.
"It became clear to us that the court has not given itself the aim of establishing the truth," she told Ukraine's Higher Administrative Court.
"Under these circumstances, we simply do not see the reason for continuing with this case being considered. We are withdrawing our suit." Yanukovich, 59, has denied any vote-rigging by his side. He beat Tymoshenko by a narrow 3.5 percentage points in the Feb. 7 vote.
Few commentators had expected Tymoshenko to win the court action, which she launched on Friday with a plea to the 49 judges to "study carefully" the evidence before it. But her sudden announcement on Saturday took most people by surprise all the same.
With her hair plaited in her trademark peasant braid, she looked tired and tense on Saturday as she announced her climb-down after months of battling with Yanukovich for the leadership of the former Soviet republic of 46 million.
But she refused to concede his victory had been honestly won and a deputy of her BYuT political bloc said it would boycott his swearing-in next Thursday.
"A fraudulent vote took place and the will of the people was fraudulently handled. Sooner or later, an honest prosecutor's office and an honest court will come to the view that Yanukovich was not elected president of Ukraine and that the will of the people was falsified," she said.
Tymoshenko had been pressing for a new presidential vote as took place in the 2004 "Orange Revolution" which ended with President Viktor Yushchenko being elected. Yanukovich was denied the top job then by the protests against electoral fraud.
Some of the ground had been cut from under Tymoshenko by Western governments which quickly congratulated Yanukovich on his victory and privately urged her to gracefully accept defeat.
Yushchenko, once her Orange Revolution ally and now her political foe, added to pressure on her on Saturday by also telephoning Yanukovich and congratulating him as the legitimately elected president-to-be.
Her change-of-heart may have been caused by the sudden realization that she was consistently losing ground.
"Tymoshenko's decision was motivated by the fact that she realized she had no prospects by this court action. By withdrawing her action, she has in fact recognized Yanukovich's victory," analyst Vadim Karacayev said.
Some of her advisers had warned her that she could damage her huge standing by refusing to bow to the inevitable and had urged her save her energies for a future in opposition.
In the past few weeks, she has lost one battle after another against Yanukovich who, while not a great public performer himself, is backed by wealthy industrialists who have organized a strong team of strategists for him.
On one occasion, she threatened to wage a second Orange Revolution to bring people out on to the street if she felt the vote had been rigged. But she drew jeers from her rivals when she later publicly backed down on the threat.
Her climb-down defused much of the political tension which has gripped the country and it seemed likely to be welcomed by investors who are anxiously awaiting the return of political stability in Ukraine.
The country, whose economy took a battering in the global downturn with its valuable steel exports losing markets, has been relying on a $16.4 billion bail-out program from the International Monetary Fund.
This has been suspended because of breached promises, but is expected to resume once political stability returns.
Tymoshenko is now likely to switch her energies to the political fight against Yanukovich, whose supporters in parliament on Friday took the first steps to force her out as prime minister.
After a bitter campaign of smears and insults, Yanukovich has ruled out any alliance with her and has asked her to quit.
She has refused and can be replaced only when the Yanukovich camp has managed to forge a new coalition among the fickle deputies of Ukraine's parliament - normally a long and tricky task. If he fails to do this, he may be forced to call early parliamentary elections.
