This group contains some of the world's largest birds - such as the extinct giant moa of New Zealand and elephant birds of Madagascar.
The different ratite species were long thought to have formed independently as the flightless birds were isolated by the separation of the southern continents over the last 130 million years.
However, ancient DNA extracted from bones of two elephant birds held by the Museum of New Zealand, Te Papa Tongarewa, revealed a close genetic connection with the kiwi, despite the striking differences in geography, morphology and ecology between the two.
Professor Cooper said the finding was as "bizarre as you can get".
"[The kiwi] looks nothing like [the elephant bird], it's on the other side of the world."
Kieren Mitchell, PhD candidate with ACAD, who performed the work, also said the findings proved a real surprise.
"New Zealand and Madagascar were only ever distantly physically joined via Antarctica and Australia, so this result shows the ratites must have dispersed around the world by flight."
The researchers now believe that both the kiwi and giant elephant bird were descended from a small flying bird, which probably flew here from a source population in Antarctica at a time the continent was more hospitable.
The results correct previous work by Professor Cooper conducted in the 1990s, which had shown the closest living relatives of the kiwi were the Australian emu and cassowary.
"It's great to finally set the record straight, as New Zealanders were shocked and dismayed to find that the national bird appeared to be an Australian immigrant," Professor Cooper said.
"I can only apologise it has taken so long."
The team were able to use the elephant bird DNA to estimate when the ratite species had separated from each other.
The evidence suggested flying ratite ancestors dispersed around the world right after the dinosaurs went extinct, before the mammals dramatically increased in size and became the dominant group.
The researchers believe the ratites exploited that narrow window of opportunity to become large herbivores, but once mammals also got large, about 50 million years ago, no other bird could try that idea again unless they were on a mammal free island - like the Dodo.
"We can now see why the evolutionary history of the ratites has been such a difficult problem," said study co-author Professor Mike Lee, of the South Australian Museum and University of Adelaide.
"Many of them independently converged on very similar body plans, complicating analysis of their history."
Dr Trevor Worthy of Flinders University in Adelaide, another co-author, said fossils of small kiwi ancestors had been recently found, suggesting they might have had the power of flight not too long ago.
"The genetic results back up this interpretation, and confirm that kiwis were flying when they arrived in New Zealand."
It also explained why the kiwi remained small, he said.
"By the time it arrived in New Zealand, the large herbivore role was already taken by the moa, forcing the kiwi to stay small, and become insectivorous and nocturnal."
Further to this "raw deal", Professor Cooper said, the abnormal size of the kiwi's egg was also likely explained by the environment it lived in then.
Long before humans arrived in New Zealand, the bird had to be wary of aerial predators, such as the Haast's eagle.
Therefore, by having large eggs, the kiwi's chicks could be large enough to be advanced by the stage they hatched, he said.
As for the giant elephant bird, the species went extinct probably in the 17th or 18th century, likely as a result of humans discovering them, Professor Cooper said.
"You've got KFC on steroids and a whole bunch of people turning up, it's not a good picture ... they were going to be the first to go."
Professor Cooper found it amusing that he had travelled to every museum in the world - between 15 and 20 of them - which he thought would have the giant elephant bird bones he needed for the study, yet the specimens that would prove key turned out to be under his nose at Te Papa.
"It turned out, ironically, that the museum right next door had some of the best material."
That they were found in New Zealand likely suggested they had been traded for moa bones, which were internationally sought after.
Professor Cooper said Dr Worthy, a moa expert who as recently as December suggested the kiwi's ancestor that flew in from Australia, "just about choked" when he revealed the findings of the study to him over lunch.
Alan Tennyson, curator of vertebrates at Te Papa, said the kiwi was an integral part of our culture and heritage.
"It's fitting that Te Papa's scientific collections have been used to resolve the mystery of its origins."
