The earthenware jars containing residual wine compounds were found in two sites south of the Georgian capital, Tbilisi, researchers said.
Some of the jars bore images of grape clusters and a man dancing.
Previously, the earliest evidence of wine-making was from pottery dating from about 7000 years ago found in north-western Iran.
The finds were published in the journal Proceedings of the National Academy of Sciences (PNAS).
"We believe this is the oldest example of the domestication of a wild-growing Eurasian grapevine solely for the production of wine," said co-author Stephen Batiuk, a senior researcher at the University of Toronto.
"Wine is central to civilisation as we know it in the West. As a medicine, social lubricant, mind-altering substance and highly valued commodity, wine became the focus of religious cults, pharmacopoeias, cuisines, economies and society in the ancient Near East."
The pottery jars were discovered in two Neolithic villages, called Gadachrili Gora and Shulaveris Gora, about 50km south of Tbilisi, researchers said.
Telltale chemical signs of wine were discovered in eight jars, the oldest one dating from about 5980 BC.
Large jars called qvevri, similar to the ancient ones, are still used for wine-making in Georgia, said David Lordkipanidze, director of the Georgian National Museum who helped lead the research.
Mr Batiuk said the wine was probably made in a similar way to the qvevri method today "where the grapes are crushed and the fruit, stems and seeds are all fermented together".
Previously, the earliest evidence of grape wine-making had been found in the Zagros Mountains of Iran and dated to 5400-5000 BC.
The world's earliest non-grape based wine is believed to be a fermented alcoholic beverage of rice, honey and fruit found in China and dating to about 7000 BC.
Photo: AFP A neolithic jar from Khramis Didi-Gora, Georgia.