The first real concessions by Yanukovich since the crisis erupted two months ago brought cries of 'Hurrah!' from several thousand demonstrators on Kiev's Independence Square, focal point of the protests.
But opposition leaders said they would continue to harness street power to wring even more gains from Yanukovich.
"We have to change not only the government, but the rules of the game as well," declared boxer-turned-politician Vitaly Klitschko. "We are sure the struggle will continue," he said.
The 66-year-old Azarov tendered his resignation as parliament met for an emergency session to work out a deal that would satisfy the opposition and end protests in the capital Kiev and in other cities in which six people have been killed.
Yanukovich quickly accepted his resignation and that of his cabinet. Azarov's spokesman said first deputy Prime Minister, Serhiy Arbuzov, a former central bank chief, would step in as acting prime minister while other ministers would stay on in an acting role until a new cabinet had been formed.
Azarov, a loyal lieutenant of Yanukovich since the latter was elected to power in February 2010, said he was stepping down to help find a political compromise "for the sake of a peaceful settlement of the conflict."
But in reality he has been publicly humiliated by Yanukovich's offer at the weekend to give his job to former economy minister Arseny Yatsenyuk, another opposition leader, in an effort to stem the rising protests against his rule.
The opposition has been calling consistently for the resignation of the Azarov government since the crisis started.
But opposition leaders have shied away from the offer of top government posts by Yanukovich, seeing it as a trap intended to compromise them in front of their supporters on the streets.
Yatsenyuk, one of a "troika" of opposition leaders, formally turned down the offer of the top government job on Monday night.
The steward of the heavily-indebted economy through hard times and recession, Azarov backed the decision in November to walk away from a free trade agreement with the European Union - the move which sparked the mass street protests.
And it was Azarov who took the heat in parliament, defending the need for closer economic ties with Russia in a stormy debate with the opposition.
Parliament went into emergency session on Tuesday with ministers loyal to Yanukovich saying they would press for a state of emergency to be declared if the opposition leaders did
not rein in protesters and end occupation of municipal and government buildings across the country.
But then Yanukovich loyalists - clearly under pressure from the president and his aides to make a U-turn - voted to repeal anti-protest legislation they had rammed through on January 16.


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