His friends became concerned when the man failed to arrive and used their hired mountain radio to raise the alarm around 6.30 last night.
Sergeant Judd said weather conditions were such that searchers were unable to get into the area last night, and the Alpine Cliff Rescue Team was flew in early this morning.
"The team sighted a body at the base of a bluff. It appears the man has slipped and tragically fallen to his death."
The victim has been flown to Fox Glacier and the rest of the party were flown to Franz Josef.
Police have contacted the man's next of kin but are unable to release his name at this stage.
The incident follows the deaths 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.
The pair were on one of their regular climbing holidays in New Zealand and had been missing since December 28.