(Transcript from World News Radio)
It comes after three months of protests in the capital, Kiev, since Mr Yanukovch rejected a European Union pact in November in favour of closer ties with Russia.
The unrest has left almost 100 protesters dead, and the country divided.
Zara Zaher reports.
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Ukraine's politicians have appointed Parliament Speaker Oleksandr Turchynov as Interim President until new elections are held on May 25.
Before leaving the country on Saturday to an undisclosed destination, Viktor Yanukovych, insisted he remained in charge.
"I'm not going to leave the country. I'm not going to resign. I'm a legitimately elected President. I've been given guarantees by all the international mediators with whom I worked. They've given security guarantees. I'll see how they're going to this part. Everything that's taking place today is to a large extent vandalism and banditry in the state coup."
One of Ukraine's opposition leaders Vitaly Klitschko has told the BBC, he believes the country urgently needs a new President with a clear mandate from the people.
"Millions of Ukrainians want to know- where is Yanukovych and let us try to find him. He disappeared. The President of Ukraine disappeared. That's why we have to elect a new one."
Opposition leader Yulia Tymoshenko, who was freed from jail on Saturday, has ruled out becoming Prime Minister again.
Ms Tymoshenko received a rapturous welcome as she arrived at Independence Square in Kiev, in a wheelchair, praising the protesters and paying tribute to those killed during the unrest.
The former Prime Minister addressed a 50,000-strong crowd before breaking down in tears.
"I dreamt to see your eyes. I dreamt to see all these forces that change this country. I just couldn't recognise this city - the barricades, the burnt houses, cars - but this country is now free. This is a country of free people and this is your victory. You gave this the freedom. The people that were were, the people that died here are the heroes."
Ukrainian demonstrators continued to occupy Kiev, even after President Viktor Yanukovych signed a reconciliation agreement with the opposition on Friday.
Mr Yanukovych promised to form a national unity government, saying a presidential election would be held by December.
But SBS Dutch correspondent Joost Bosman, who's in Kiev, says there was a sceptical reaction to the deal on the streets.
"People are not happy, not happy enough with what happened today with agreement between the government and the opposition, so they don't leave the barricades. They are willing to fight and they will stand on the barricades and they will continue until the moment that President Yanukovych will step down."
This protester echoed that view, saying demonstrations would continue until the resignation of Mr Yanukovich.
"We are positive for the current result, but our basic requirement still is to ask Yanukovych to resign. If this requirement is not satisfied, protesters will not be satisfied."
In Mr Yanukovich's stronghold areas of the east and south of Ukraine, his departure is viewed as a coup.
At a convention on Saturday, the leaders of mainly Russian-speaking regions, loyal to Mr Yanukovich, have challenged the legitimacy of the national parliament and say they will take control of their territories.
One of their fears is that the new government may outlaw the Russian language.
Following his appointment as acting President, Oleksander Turchinov said his government was ready to talk to the leadership of Russia to try to improve relations.
But he made it clear that the country's return to European integration would be a priority.
International leaders have urged Russia not intervene in Ukraine.
British Foreign Secretary William Hague has told the BBC, it will be in Russia's interests for Ukraine becoming closer to the European Union.
"It's very important for us to continue to try to persuade Russia that this need not be a zero-sum game. It's in the interest of the people of Ukraine to be able to trade more freely with the European Union- it's in the interest of the people of Russia for that to happen as well."
The United States says the conflict in Ukraine should not be seen as a tug of war between East and West or the United States and Russia.
It says Ukraine's future should reflect the will of the Ukrainian people, without intervention by Russia.
European Union foreign policy chief, Catherine Ashton says the future for Ukraine remains difficult.
"It's very important that this violence stops and that we begin to see a move forward. This is about European Union, in our neighbourhood, actually working with the people and the politicians of Ukraine to try and ensure a stable and prosperous future for all of them."
