Yanukovich abandoned the capital to the opposition on Saturday and denounced what he described as a coup after several days of bloodshed this week that claimed 82 lives. (Agencies)
Supporters cheered former prime minister Tymoshenko as she left the hospital where she had been held. When she spoke later in Kiev, her reception was mixed.
Her release marks a radical transformation in the former Soviet republic of 46 million people. Removal of the pro-Russian Yanukovich should pull Ukraine away from Moscow's orbit and closer to Europe.
It is also a reversal for Russian President Vladimir Putin's dream of recreating as much as possible of the Soviet Union in a new Eurasian Union. Moscow had counted on Yanukovich to deliver Ukraine as a central member.
Members of the Ukrainian Parliament, who abandoned Yanukovich after this week's bloodshed, applauded and sang the national anthem after declaring him constitutionally unable to carry out his duties. An early election was set for May 25.
"This is a political knockout," opposition leader and retired world boxing champion Vitaly Klitschko told reporters.
In a television interview the station said was conducted in the northeastern city of Kharkiv, Yanukovich said he would not resign or leave the country, and called decisions by Parliament "illegal".
"The events witnessed by our country and the whole world are an example of a coup d'etat," he said, comparing it to the rise of the Nazis to power in Germany in the 1930s.
Interfax news agency said border guards refused to let Yanukovich exit the country when he tried to fly out from the eastern city of Donetsk.
At Yanukovich's abandoned secret estate a short distance from Kiev, people flocked to take photographs of his private zoo with ostriches and deer, replica ancient Greek ruins, and lavish waterways and follies.
Despite Yanukovich's defiance, the dismantling of his authority seemed all but complete. His cabinet promised a transition to a new government, the police declared themselves behind the protesters and his arch-rival Tymoshenko went free.
Tymoshenko, with her trademark braided hair, waved to supporters from a car as she was driven out of the hospital in Kharkiv, where she has been treated for a bad back while serving a seven-year sentence since 2011.
Setting herself immediately on a collision course with Moscow, Tymoshenko said she was sure her country would join the European Union in the near future. Her release was welcomed by Washington.
Russian Foreign Minister Sergei Lavrov said "illegal extremist groups are refusing to disarm and in fact are taking Kiev under their control with the connivance of opposition leaders".
As night fell, 30,000 opposition supporters on Kiev's Independence Square, scene of nearly three months of protests, were in buoyant mood.
There was sadness too, with coffins displayed in front of the crowd as priests said prayers. People crossed themselves in front of makeshift shrines with candles and pictures of the dead. Two captured water cannon trucks were parked in the square like trophies of war.
Carried on to a stage in a wheelchair, an emotional and tired-looking Tymoshenko told the protesters on the square, known as the Maidan: "You have no right to leave the Maidan ... Don't stop yet.
Showing glimpses of the fiery orator that drove her to power, Tymoshenko shouted: "This is a Ukraine of different people. The ones who died on Maidan are our liberators, our heroes for centuries."
The response was mixed. Tymoshenko is a divisive figure in Ukraine, where many have become disillusioned with a political class they see as corrupt and elitist.
Small pockets of the crowd clapped and sang Tymoshenko's name, but the chants did not catch on. Whistles could be heard. Others listened silently.
Earlier, the Ukrainian cabinet said it was committed to a responsible transfer of power. Military and police leaders said they would not get involved in any internal conflict.
Yanukovich enraged much of the population by turning away from the European Union to cultivate closer relations with Russia three months ago. On Friday, he made sweeping concessions in a deal brokered by European diplomats after days of street battles during which police snipers gunned down protesters.
But the deal, which called for early elections by the end of the year, was not enough to satisfy pro-Europe demonstrators on Independence Square. They wanted Yanukovich out immediately in the wake of the bloodletting.
The release of Tymoshenko transforms Ukraine by giving the opposition a single leader who may become president, although Klitschko and others also have claims.
Tymoshenko, 53, was jailed by a court under Yanukovich over a natural gas deal with Russia she arranged while serving as premier before he took office. The EU had long considered her a political prisoner, and her freedom was one of the main demands it had for closer ties with Ukraine during years of negotiations that ended when Yanukovich turned towards Moscow in November.
She had served as a leader of the "Orange Revolution" of mass demonstrations which overturned a fraudulent election victory for Yanukovich in 2004, but after a divisive term as prime minister she lost to him in an election in 2010.
Yanukovich abandoned the capital to the opposition on Saturday and denounced what he described as a coup after several days of bloodshed this week that claimed 82 lives.