A team-mate was lowered down the 30-40m crevasse to retrieve him using a pulley system.
"The soldier was recovered by his colleagues who administered first aid," the Department of Defence said in a statement last night.
"Sadly, they were unable to revive him and the New Zealand emergency services later declared the soldier deceased."
Alpine guide Trevor Streat was called in to help the rescue effort and said emergency services were alerted about 12.20pm when a member of the group "raised the alarm" from the Department of Conservation's Plateau Hut, about 45 minutes by foot from the scene.
The Grand Plateau was beneath the east face of Mt Cook and could be tricky to navigate due to the mix of ice and snow in the area, Mr Streat said.
"Basically, the Grand Plateau is like a lake. You get this area, even though it's quite flat, where there's lots of crevasses because the ice is speeding up and going down the Hochstetter Ice Fall."
The conditions created a "slightly elevated danger of crevasse fall" compared to other areas on Mt Cook, Mr Streat said.
"You've got ice underneath one or two metres of winter snow, and there's been quite a lot of snow and wind lately so the crevasses get these bridges over them.
"If you're unlucky one can break underneath you -- that's what happened to this guy."
The dead soldier was highly qualified and experienced in alpine, mountain and altitude activities, the Australian Department of Defence said.
Mr Streat said the men were "very well equipped".
"They were also trained to the point where they could go down the crevasse and rescue their friend which is actually quite a difficult thing to do in the circumstances."
The New Zealand Defence Force was not involved with the training. A spokesman said its thoughts were with its Australian counterparts as they dealt with the tragedy.
More than 200 people have died in the Aoraki/Mt Cook National Park.
Yesterday's death has been referred to the Coroner.