"We will eliminate the financial problems created by the previous government," he said.
"The country has been plundered, the coffers are empty, state debt has risen threefold ... The main task today is to redraft and get approved a realistic budget."
The ex-Soviet republic, battered by the economic downturn, needs a new government to adopt a delayed 2010 budget and restart talks with the International Monetary Fund on a suspended $16.4bn bail-out package.
Tymoshenko's departure as prime minister following a no-confidence vote marks the end of five years of rule by the leadership which emerged from the 2004 pro-Western Orange Revolution.
Yanukovych's Regions Party said it expected a full government line-up to emerge on Thursday, likely headed by the Russian-born Azarov.
Born in Russia and resident in Ukraine since only 1984, Azarov is seen as a safe pair of hands though no radical reformer.
Although Tymoshenko has refused to recognise Yanukovych's legitimacy, she appears to be positioning herself as a strong opposition leader against what she describes as the "anti-Ukrainian" policies of the president.