Miles Vinar 42, from Perth, was found safe on Saturday on New Zealand's highest peak, after another mountaineer spotted him.
Senior Constable Les Andrew from Omarama Police said Vinar spent two harrowing nights in a snow cave after watching helplessly as his brother, Dr Mark Vinar, plunged to his death.
When rescuers reached Miles they realised how close he had come to dying, too, Mr Andrew said.
"The rescue guys were saying he was just metres away from a moving avalanche," he said.
"He would have been buried if his snow cave was just a few metres away." Mr Andrew said after the rescue Miles was okay physically, but emotionally exhausted over his brother's death.
The two climbers had flown to Plateau Hut, on Mt Cook, last Saturday, and set off to climb the mountain on Wednesday at 1am.
Although initially expecting to return the same day, they decided to remain on the mountain and became stuck on a ridge.
They decided to return to the hut on Thursday morning, which was when they ran into trouble, Mr Andrew said.
"They had gone past the tricky part... there is a bit of a snow shelf that drops off vertically," he said.
"Miles he was fine coming down. He said it was technical, but it was do-able, it wasn't dangerous.
"His brother started to climb down as well but the next thing he knows his brother is falling backwards, he (Mark) has lost his grip and tumbled down probably 500 metres plus and sort of rolled down the hill. Miles had sight of him initially, but he disappeared," he said.
After watching his brother's presumed death Miles spent two nights on the snow-swept part of the mountain, surviving on chocolate bars.
"He has stopped there, dug himself into the snow with an ice axe and stayed the night up there. He said it was a horrific night. It was snowing and snow was sliding around him. He had a busy night keeping the snow clear of him and his airways clear," Mr Andrew said.
"He spent the day there. He couldn't signal anyone, because it was so thick with cloud and stuff," he said.
Neither climber carried an emergency beacon and Mr Andrew said they had only light supplies, because they did not intend to spend the night in the area.
Miles was in remarkably good condition when found, and despite his ordeal wanted only chocolates and a hot shower.
Mr Andrew said Miles understood the search for his brother had been abandoned and the body would not be recovered.
"He was quite good about that. He thinks his brother would probably want that. If he was in the same situation, it is what he would want," he said.
The brothers have been described as moderately experienced mountaineers - Mark has climbed peaks in Bolivia.
It is believed they were in training to eventually climb a mountain in Alaska.
In a statement, the family of the two men said Mark would be deeply missed.
"We are still in shock about the recent passing of Mark. He was doing something he loved and was with someone that loved him very much," the statement said.
"Miles has spoken of Mark's joy for what he was doing and has also praised the amazing job that the rescue team that acted so promptly to bring him out," it said.
"At this time we ask for privacy for Mark's immediate family and friends, in particular his adored girls." The route the brothers took to climb Mt Cook is seen as one of the more dangerous routes to ascend the mountain.
Nine people have died on Zurbriggens Ridge, where Mark is thought to have perished, and 70 people have died on Aoraki/Mt Cook since 1907.
Thirty-four Australian climbers have died in the Aoraki/Mt Cook National Park, including 18 on the mountain.
