The bones were sealed beneath a layer of ash from the Taupo eruption meaning they were at least 1800 years old.
Mr Adds said the moa had not had human contact and may have become trapped in the swamp.
"It is a big find." Mr Adds said the bones were currently at Te Papa but some would be returned to local iwi. "It's generated a whole lot of interest." The bones would be studied further.
Whanganui Regional Museum natural history curator Mike Dickison said it sounded a similar environment to the Makirikiri swamp near Wanganui where most of the museum's collection of moa bones was found in the 1930s. "I guess it tells us that the moa population up there was actually very similar to what it was down here almost at the water's edge."
He said the forest would have extended up to the Taihape area. "It would've been a bit more like that Whanganui National Park."
The university group is going back in a few weeks to collect more bones.