Adult females were among the tuatara translocated to Orokonui Ecosanctuary from Takapourewa-Stephens Island in October 2012.
"At least two of the adult females must have been carrying shelled eggs when transferred, as they nested soon afterwards," research team member Dr Anne Besson said.
"On Stephens Island, eggs hatch about 11-16 months after laying, after one winter in the ground. But when we checked the eggs at Orokonui previously, at the end of the summer about 15 months after laying, the eggs were still incubating."
The researchers continued to check on the nests and, at the end of last month, they found the evidence they were hoping for.
An excavated nest contained three empty eggshells with the characteristic splits that hatchlings make to exit the shells. Some other eggs had collapsed and failed.
Research team leader Dr Alison Cree, an associate professor at the University of Otago, said the discovery provided the first indication that tuatara eggs could hatch after a "remarkable" two winters in the ground.
Dr Cree said the timing supported Dr Besson's earlier work, which suggested that cool soil temperatures at Orokonui could slow development.
"With New Zealand reptiles, you have to be in for the long haul, unlike many birds where nesting success may be apparent within a few weeks or months," she said.
Sanctuary staff were delighted with the news and were looking forward to the hatchlings becoming more visible as adults in about 15 years' time.
Orokonui Ecosanctuary general manager Chris Baillie commented: "Although these hatchlings are not able to be seen by the public, two young captive-bred tuatara are often seen basking in a special enclosure near the Ecosanctuary entrance."
The research team now has thousands of images from time-lapse cameras to check to try to detect the time of hatching more precisely.