The EU imports about a quarter of its gas from Russia.
Gazprom began pumping gas into Ukraine on Tuesday morning from the Sudzha metering station on the border.
Several hours later, the gas reached Ukraine's western border with Slovakia, then Hungary, Bulgaria and Moldova - some of the countries worst hit by the disruption to supplies because of their dependence on Russian gas.
We will be fully satisfied after three or four days of supplies to Europe
By Wednesday morning, officials had reported deliveries in other affected nations further down the pipeline.
Only Greece has yet to report the resumption of supplies, but is expected to receive gas soon.
The Czech Republic, the current holder of the EU presidency, said it would take several days of supplies at normal levels for the crisis to be considered over.
"We will be fully satisfied after three or four days of supplies to Europe," Czech Industry Minister Martin Riman said on Tuesday.
Gas flows were resumed after Russia and Ukraine finally agreed prices at which Ukraine would buy Russian gas, and ship it to Europe.
Previously Ukraine has paid a heavily discounted rate. But the Russian state energy company, Gazprom, confirmed that Ukraine would start paying the market rate - with a 20% discount for the rest of 2009.
Russia and Ukraine say they have signed a 10-year agreement
Gazprom said that would initially mean a fee of $360 per 1,000 cubic metres.
That compares to the market rate paid by European customers of about $450 - but is a major hike for Ukraine, which until December was paying only $179.50.
However, the price will drop in line with falling gas prices. By midsummer, Ukraine could be paying as little as $150, one expert said.
Ukrainian Prime Minister Yulia Tymoshenko said Kiev would end up paying less than $250, on average, over the course of 2009.
A spokesman for Ukrainian President Viktor Yushchenko said he was "disappointed and devastated" by the deal, but would not block it.
Although the new contract lasts for 10 years, the fine-print remains unknown - leading to fears that the row could flare up again in the future, says the BBC's Gabriel Gatehouse in Kiev.
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