He was James Poland (48), from West Launceston, Tasmania.
A Te Anau police spokeswoman said Mr Poland was an experienced tramper, but ill-equipped for the terrain.
He had plenty of warm clothing and a locator beacon for his tramping trip, but he had not taken any ropes with him.
She said the area was not suitable for tramping.
Rather, it was a place for experienced climbers.
His body was found by a search and rescue helicopter crew in the mountainous Lake Adelaide area on Sunday afternoon.
Sergeant Brock Davis, of Invercargill, said it appeared Mr Poland died after a fall at Barrier Knob, about 3km north of Homer Hut.
Mr Poland set off on a lone three-day tramp over Gertrude Saddle on Thursday, planning to emerge at lower Hollyford Rd on Sunday.
He was holidaying in New Zealand with his wife and children.
His wife raised the alarm when he failed to return on Sunday.
It was likely he had fallen on the first day of his tramp, Mr Davis said.
