The man, named by Swedish authorities as Magnus Kastengren (32) had been skiing near the mountain's lower summit, at an altitude of about 3700m, when he slipped off a ridge and fell.
His 30-year-old companion - thought to be experienced Swedish ski-mountaineer Andreas Fransson - only realised what had happened when he looked back to see his partner had gone.
Locals who know the mountain well said the pair's skiing was ''extreme'' and there was no room for error.
Only four days earlier, the Swedes were thought to have become the first skiers to complete a continuous descent of Mt Cook's east face.
The feat, with New Zealand-based skiers Nick Begg and Tyrone Low, was only the second attempt to ski down the face.
Senior Constable Brent Swanson, of Lake Tekapo, said the men had been skiing along Mt Cook's summit ridge, near the lower peak, yesterday morning when one of them fell 600m vertically down the steep slope.
''One minute his partner was skiing behind him, and next minute he's looked back and he's gone. Basically, he's slipped off and we don't know why.''
Snr Const Swanson said skiing along the ridge was ''right up there at the extreme level''.
''These guys were extreme skiers. That's their job, that's what they do.
''They've had a number of firsts and successes, apparently, with high alpine skiing,'' he said.
''This wasn't unusual for them. But obviously something tragic has gone on.''
The survivor had ''a bit of a scare'' but was uninjured.
Snr Const Swanson said climbing conditions had been good and the weather was fine at the time.
A Department of Conservation alpine rescue team was dispatched after the survivor called emergency services about 8.30am yesterday.
A rescuer, suspended on a strop from a Helicopter Line helicopter, picked him up shortly before noon.
Mr Kastengren's body was recovered about half an hour later.
Doc Mt Cook alpine rescue team leader Jim Spencer, an alpine ski guide for 15 years, said skiing on the mountain could be very dangerous and there was no room for error.
''In the alpine regions, there's not always safe run-outs that you typically get at a ski hill,'' he said.
''If you were to slip, you would very quickly pick up a speed that you couldn't control.''
Mr Spencer said the pair's accomplishment on the east face last week - which he probably would not attempt himself - was ''very, very credible alpine skiing''.
''Those boys were at the top of their game, I'd say.''
Mr Spencer said the pair had climbed to the summit from Plateau Hut. From there, they travelled along the summit ridge towards the lower peak.
The man fell somewhere between the middle peak and Porter Col, the lowest point between the middle and low peaks.
Mr Spencer said the pair might have been intending to descend the mountain through the Hooker Valley.
Swedish honorary consul to New Zealand Frank Olsson said a police officer had named the man as Mr Kastengren.
He said officials in Stockholm had been trying to get in touch with Mr Kastengren's family in Sweden, but he had not received confirmation his relatives had been reached. Both Swedes have been involved in a number of ski-mountaineering firsts, with Mr Kastengren accompanying Mr Fransson on the first descent of the south face of Denali in Alaska.
Mr Fransson has also had firsts on mountains in Scandinavia and and North America.
His website said his skiing might appear ''reckless'' but his ''consistent performance on life-threatening lines is actually founded in a hyper-focused, zen-like devotion to training and the understanding of skiing's micro-mechanics''.
