He was Rangiora man Eric Jacomb (54).
His death occurred a day after two Australian trampers died in Aoraki/Mt Cook National Park.
Sergeant Sean Judd, of West Coast police search and rescue, said the North Canterbury man fell from the Mawson Glacier near the headwaters of the Whataroa River. It is believed he slipoped on ice and fell.
• Couple shared a love of climbing
Mr Jacomb was one of a party of five people tramping in the area. He had separated from his companions yesterday and was supposed to meet them later in the day at the Top Butler Hut.
His friends became concerned when he failed to arrive and used their hired mountain radio to raise the alarm about 6.30pm.
Sgt Judd said bad weather prevented members of the South Westland Alpine Cliff Rescue team getting to the scene last night. The team was flown in early this morning, spoke to the rest of the party at the hut and then flew over the area.
"The team sighted a body at the base of a bluff. It appears the man has slipped and tragically fallen to his death.
"It was a technical recovery and we certainly needed the team's skills in this type of terrain."
The body had been flown to Fox Glacier and the rest of the party were flown to Franz Josef.
The death follows those of Australian couple Stuart Hollaway and Dale Thistlethwaite who fell, roped together, more than 700m down a steep face on the eastern slope of Mt Silberhorn in the Aoraki/Mt Cook National Park.
Their bodies were recovered yesterday. They were on one of their regular climbing holidays in New Zealand and had been missing since December 28.
