"The company is ready to fulfil the daily requests of its European customers."
Tymoshenko said the "historic" agreement would prevent future disputes over the price of gas paid by Ukraine.
She said Europe would receive supplies "as soon as the gas enters Ukraine's gas pipelines. There won't be any delay".
Tymoshenko said Kiev would pay less than $250 per 1,000 cubic metres of Russian gas in 2009, adding that she expected supplies to Europe to resume within hours.
The office of Ukraine's president criticised the deal, saying it handed victory to Moscow and would damage the Ukrainian economy.
Viktor Yushchenko's energy adviser, Bohdan Sokolovsky, said on Monday that by agreeing to pay higher rates for Russian gas this year without increasing the amount it charges Russia for gas transit to Europe, Ukraine would be "subsidising" Gazprom, the state-run Russian gas giant.
"We are giving Russia a more than 60 per cent discount on transit to Europe. ... We will be subsidising Gazprom," he told the Interfax news agency.
Separately, the deputy leader of Ukraine's leading opposition party, the Regions Party, told Interfax that the deal was a defeat for the Ukrainian government because it would lead to gas prices of more than $300 per 1,000 cubic metres.
"A price of more than $300 for gas for Ukrainian companies ... is a defeat for the Ukrainian government's entire energy policy," Anna German said.
The European Commission (EC) has remained cautious over the Ukraine-Russia deal, demanding to know precisely when gas taps will be turned back on, and said monitors would assess the supplies.
"We now need an indication of the precise time that gas deliveries will be resumed. Our monitors will verify when the gas actually starts to flow," an EC statement said.
Earlier, Johannes Laitenberger, an EC spokesman, said: "For the time being, no gas is flowing. There is no reason why it should not flow."
"We understand that Russia and Ukraine need to finalise their agreement ... In any event let me be clear, the proof of the pudding is in the eating and the proof of the gas is in the flowing," he said.
Martin Riman, the Czech Republic's industry minister, whose country holds the EU presidency, said he was only "slightly optimistic" about the deal.
"If the deliveries don't resume despite such strong declarations by the Russian and Ukrainian prime ministers, there will be a total crash in the confidence of EU consumers, citizens and the enterprise," he said.
Naftogaz, the Ukrainian state energy company, said it would take up to a day and a half to pump gas to its western border once Russia resumes the service.
Russia cut shipments of gas to Ukraine on January 1, after the dispute over prices stalled the renewal of a gas agreement between the countries.
It then halted all gas shipments to Europe via Ukraine on January 7, alleging that Ukraine was siphoning off Europe-bound gas.