Gazprom had cut supplies by a quarter on Monday and a further quarter on Tuesday amid a dispute over Ukraine's $600 million debt for gas supplies.
Sergei Kupriyanov told reporters: "Gas transit through Ukraine for European consumers is being implemented in full. Restrictions on gas supplies to Ukrainian consumers have been lifted."
Ukrainian state oil and gas company Naftogaz confirmed that supplies had been resumed in full.
"Gazprom has resumed gas supplies. I believe that supplies will reach full capacity by tomorrow, as some time is needed for the gas transportation system to resume its normal regime," a Naftogaz spokesman told RIA Novosti.
Kupriyanov said supplies had been resumed after Gazprom CEO Alexei Miller and Naftogaz chief Oleh Dubina reached an agreement in negotiations by phone.
"The sides agreed that gas supplies provided from January 1 to March 1 2008 would be fully documented and paid for by Naftogaz Ukrainy in accordance with the scheme in place since the start of the year. Issues relating to the supply of Russian gas will be resolved," he said.
Ukrainian President Viktor Yushchenko gave assurances earlier on Wednesday that Ukraine would not reduce Russian gas transit shipments to Europe despite the gas cuts to Ukraine.
