supply run from the South Pole to Italy's Antarctic base at Terra Nova Bay.
After efforts to reach the plane were frustrated for four days due to bad weather, helicopters late on Saturday reached the crash site in the Queen Alexandra mountain range.
"The site of the crash is at a height of 3,900 metres (13,000 feet) at the northern end of the Queen Alexandra Range," the Rescue Coordination Centre New Zealand said.
"The aircraft wreckage is on a very steep slope, close to the summit of Mount Elizabeth. It appears to have made a direct impact that was not survivable."
Centre coordinator Tracy Brickles said it was a sad end to the rescue effort.
"It has been a difficult operation in challenging conditions but we remained hopeful of a positive result. Our thoughts are now with the families of the crewmen," Brickles said.
The plane belonged to Canada's Kenn Borek Air, a firm based in Calgary that charters aircraft to the US Antarctic programme.
It went missing in a rugged area midway between the South Pole and Terra Nova, which lie about 1,400 kilometres (870 miles) apart.
The RCCNZ said two helicopters flew over the wreckage late Saturday after setting off from a base camp 50 kilometres from the crash site, the closest they could get in the unforgiving conditions on the frozen continent.
"A landing was not possible. They were able to survey the site briefly before returning to the Beardmore Glacier site," it said.
Kenn Borek Air confirmed that visual contact had been made with the plane by search and rescue (SAR) aircraft, including a C130 Hercules of the New York Air National guard.
The sighting was then confirmed by a Kenn Borek Air Twin Otter aircraft deployed in the mission.
"The crew of the SAR Twin Otter reports that the overdue aircraft impacted a steep snow and ice covered mountain slope," it said in a statement.
"No signs of activity are evident in the area surrounding the site, and it appears that the impact was not survivable."
Helicopter crews and mountain rescue personnel will continue to attempt to access the wreckage, are waiting for more favourable weather conditions, it said.
The missing men have not been identified, although New Zealand media have named the captain as Bob Heath, an experienced polar pilot.
The RCCNZ coordinated the search, with cooperation from US and Italian authorities in Antarctica, because the Queen Alexandra range lies in its rescue zone.
It said the crew's next of kin had been notified of their death.