The stones were found on the last day of an extensive geophysical survey at an area called Da Heights. The group found stones rising from the ground in a curve which did not look like they were placed naturally.
Extensive research has shown the stones were part of an early Bronze Age ceremonial enclosure. The structure would have been built some time between 3500 and 2000BC.
Jayne Lawes, the director of excavations, said: "This excavation has proved conclusively that the stone enclosure is man made and similar in construction to others of the late Neolithic or early Bronze Age.
"The actual date of the construction has yet to be proved, though one shard of pottery has been found buried under 60cm of peat on the floor of the enclosure and should help to provide evidence of a date when the site was in use."
John Holbourn, a Bacas member from Wiltshire, said: "The alignment of the stone ring to the midwinter sunrise is of real significance.
"While in the summer the island is bathed in light throughout most of the day and night, in the winter daylight lasts for only a few hours.
"The knowledge that the days will lengthen and get warmer is very cheering."
Isobel Holbourn, who owns the land in Foula where the discovery was made, said: "We knew there was something there, and the archaeologists found an egg-shaped circle of stones.
"It turns out that the winter sunrise goes right up the middle, while the summer solstice rises at right angles to it.
"The circle is egg shaped, and in the centre they dug a trench and found a paved area and a bit of black pottery in between the stones.
"This has been sent away to be dated. The team watched the summer solstice sunrise on 21 June. From the middle spot the sun rolls and rises up the side of Ronas Hill - the highest hill on the Shetland mainland."