The team dug up tools that have been shown to date from the end of the last Ice Age.
It is the first time there has been proof that humans lived in Scotland during the upper paleolithic period.
This was a time when nomadic humans hunted giant elk and reindeer using bows and arrows, and when mammoth and rhino also roamed the land.
Flint arrowheads were discovered in a field by the Biggar Archeology Group. The tools had been made in a way that identified them as belonging to about 12,000 BC.
At that time, the North Sea was an expanse of land, around which the nomadic humans roamed. Similar tools have been found in Denmark, the Netherlands and Germany, but never before in Scotland.
Dr Alan Saville, a senior curator at the National Museum of Scotland, who helped identify the objects, said he was "very excited" when he saw them. "This is the breakthrough," he said. "Now we are able to say for absolute certain that we had human settlement at that time in Scotland."
He added: "Of course, it must be remembered that most of the North Sea was dry land at 12,000 BC, probably supporting a human population that would have links both east and west.
"But to have found our first British site of this period right in the middle of southern Scotland is remarkable."
Previously, the earliest evidence of human habitation in Scotland was thought to be at Cramond near Edinburgh, which had been radiocarbon dated to around 8,400 BC.
Next month, the archaeologists will return to the spot at Howburn Farm, near Elsrickle, to carry out a larger excavation and see what else they can find.
Tam Ward, project leader from Biggar Museums, said he was "gobsmacked" when he found out how old the tools were.
The team led by Mr Ward, an electrician who has been an amateur archaeologist for 30 years, spotted the site when they noticed a large number of artefacts on the surface of the ploughed field.
This was in 2005, and at first it was assumed the items belonged to the neolithic period, dating to about 3,000 BC, making them far less extraordinary.
It was not until now that they have been officially identified as belonging to a far earlier age by Dr Saville and his colleagues, after they caught sight of a few particularly unusual tools in the collection.
A technique used to fashion the blades known as "en eperon" made it clear they belonged to the upper paleolithic period.
Aileen Campbell, south of Scotland MSP, said the find was "just incredible".
"To know there is hard evidence that human beings had settled in the Biggar area some 14,000 years ago is quite inspiring, and helps put modern life into a bit of perspective," she said.