Even as Gazprom's decision was being announced, Zurab Nogaideli, Georgia's prime minister, told a briefing in Tbilisi, however, that Azerbaijan would be the country's main supplier of gas next year.
He made no mention of a deal with Russia.
Alexander Medvedev, the head of Gazprom's export division, said that Gazprom had signed the new contract with Georgian officials.
He said: "Clouds have dispersed, the sky has cleared and we can look into the future with optimism."
Russia's relations with its neighbour have been strained since Georgia briefly detained four Russian military officers on spying charges this autumn.
In response, Moscow imposed an economic and transport blockade, and cracked down on Georgian migrants.