A colony of the rare Rugathodes sexpunctatus, which is related to the deadly Black Widow of North America, was found by arachnologists conducting research in the city's central Necropolis cemetery.
However, unlike its more venomous cousin, the spider is harmless to humans and measures just 2mm long. It was spotted living among ivy on graves and walls and at first baffled bug experts, who were carrying out a survey of the wildlife. Fittingly for an American species, it was found on the 4th of July.
The spider was only identified after a specimen was sent to an expert in Innsbruck, Austria, who was able to establish what it was. Now arachnologists are trying to work out how it made a home in Scotland.
Mike Davidson, of the British Arachnological Society, found the colony. He said: "This is an exciting find of a species which has been able to establish itself a long way from its native land. We have no idea how or when it arrived but it may have been here for many years, judging by the size of the colony.
"Although it was probably accidentally introduced with imports from North America, it is possible it arrived under its own steam ballooning on a silk thread, high in the atmosphere on a favourable wind."
Very little is known about the spider, which has not been greatly studied. It is a yellow-brown colour and is marked by a series of dots on its back, from which it takes its name. Specimens have been found in Russia, but it is more widespread in California, Arizona and Carolina.
Glasgow's Necropolis is well known for its value for wildlife and is home to a number of rare and important species.
Richard Weddle, of the Friends of the Glasgow Necropolis, said: "Its wooded areas, sandy slopes, and ivy-covered quarry-face, as well as some un-mown flowery corners provides a great diversity of habitats for wildlife."
Craig Macadam, Buglife Scotland director, said "Buglife are currently working in Glasgow to turn a number of urban green spaces into wildflower havens for invertebrates such as this spider. We hope that through our pollen and nectar rich wildflower meadow creation we can provide homes, food and shelter for a number of invertebrates."