The quolls were flown to the Jervis Bay airfield from Launceston by a chartered aircraft, accompanied by a Booderee traditional owner.
The small mammals came from the Tasmanian Quoll Conservation Program sanctuaries Devils@Cradle at Cradle Mountain and Trowunna Wildlife Sanctuary at Mole Creek.
The quolls have been restricted to the wild of Tasmania for the last 50 years due to the state's fox-free status after being eliminated from the mainland by the fox, their chief predator.
Dr Dexter said the last recorded live Eastern Quoll on mainland Australia was at Nielsen Park in Sydney in 1963 while roadkill quolls had been recovered in the Illawarra, also in the 1960s.
Dr Dexter said the quolls had been relocated now because of the work done to fox-proof the area and because of an agreement between the traditional owners and the Tasmanian government.
The animals have been fitted with collars carrying a GPS and UHF radio signal so their progress in the park can be closely monitored.
So far the animals had stayed close to their drop-off points.
"We were somewhat concerned because other species have covered a huge distance in a short amount of time. But they have not moved too far," Dr Dexter said.
The quolls did not have a long life - two to three years - but did produce a litter of about six babies once a year, the new arrivals at Jervis Bay hoped to generate a long line of animals.
The quolls are the third native species to be reintroduced to the park in recent years, following the release of long-nosed potoroos in 2014 and southern brown bandicoots in 2016.
WWF-Australia's head of living ecosystems, Darren Grover, said the World Wide Fund for Nature was excited to be involved in the project to return the "feisty but fragile" Eastern Quoll.
"This is the first time in Australia that a carnivore extinct on the mainland has been re-introduced to the wild," Mr Grover said.
"Most of the carnivores lost from the mainland are gone forever, it's not possible to bring them back, so this is a rare opportunity.
"For thousands of years eastern quolls played a part in the ecosystem as primarily insect-eaters. It will be fascinating to see what happens when they return to that role at Booderee".
Assistant Minister for the Environment Melissa Price said the Commonwealth had provided more than $2 million to Parks Australia through the Threatened Species Commissioner for projects like these.
"What I love most about this project is the very real outcomes it has had on the ground thanks to the hard work of all involved. To see potoroos, bandicoots and quolls return to a landscape they once inhabited, thanks to excellent fox and fire management, is heartening," she said.
Threatened Species Commissioner Dr Sally Box was proud to see the work come to fruition.
"Species recovery is all about partnerships, and this is another fantastic example of how governments, NGOs and the science community are working together to deliver results."
The Wreck Bay Community, the traditional owners of Booderee, has endorsed this project, while the Threatened Species Recovery Hub of the Australian Government's National Environmental Science Program has provided research and monitoring support.
Megan Doherty is a reporter for The Canberra Times
Morning & Afternoon Newsletter