Lawmakers also fired several ministers, including the foreign and education chiefs.
But who will lead the nation is still a big question.
Tymoshenko announced Sunday that she doesn't want to be considered for the nomination for prime minister, according to a statement posted on the Batkivshchyna party website.
The opposition coalition is a chaotic mix of voices, each working to assert dominance.
Former world champion boxer Vitali Klitschko has been the most well-known opposition figure during the crisis. He heads the Ukrainian Democratic Alliance for Reforms party. But the opposition bloc goes well beyond Klitschko and his party.
Then there's Arseniy Yatsenyuk, another opposition figure and former foreign minister.
Last month, the President offered a package of concessions under which Yatsenyuk would have become the prime minister and Klitschko deputy prime minister on humanitarian issues. The opposition refused.
The series of concessions started Friday with Parliament overwhelmingly approving the return of the nation's 2004 constitution. Reinstating it gives the President less power -- a key demand of protesters who'd taken over Kiev City Hall for weeks -- and paves the way for lawmakers to appoint key ministers.
Close ally Russia has been busy hosting the Winter Olympics, which end Sunday.
But it's closely linked to the crisis, which started in November, when Yanukovych scrapped a European Union trade deal and turned toward Russia.
Russia offered to lend money to Ukraine in a deal worth billions of dollars and lower its gas prices.
The deal sent protesters to the streets as Russia pressured Yanukovych to crack down on demonstrators.
On Saturday, Russia's ambassador to the United Nations, Vitaly Churkin, condemned what he called Western attempts to influence the outcome of the tumult in Ukraine.
"Either they don't understand the consequences of what they're doing, or they're engaged in a very provocative game of destabilizing Ukraine and therefore Eastern Europe," Churkin said in a post on his official Twitter account.
Churkin has accused the opposition of wanting to take power by force.
"If those so-called democratic opposition leaders come to power on the shoulders of thugs, that will not produce democracy in Ukraine," he said.
On Sunday, U.S. Secretary of State John Kerry and Russian Foreign Minister Sergey Lavrov spoke about the situation in Ukraine. According to written statement from a senior State Department official, Washington strongly prodded Moscow to accept the results of the Parliament's decisions.
Kerry also asked Russia to work with the United States and the European Union on enabling "critically needed reforms" and to not use military force in the country, which shares a border with western Russia.