Area commander Inspector Dave Gaskin said the rescue team had flown out at about 6pm, after assessing whether it would be safe.
They had retrieved the bodies using a helicopter with a long line and a person on the end, which meant they did not need to land.
'This is a high alpine area and it's extremely steep and there are some real dangers in there," he said.
However, the recovery had been successful and without any problems, he said.
Mr Gaskin said the climbers were thought to have camped near the summit of the mountain the night before their fatal fall.
They were thought to have been just 50m from their camp when something went wrong.
An ice axe was spotted dug into the mountain side about 700m above their bodies, he said.
"They're both roped together so one may have fallen and then pulled the other or they may both have fallen together, we can't figure that out at this stage," he said.
"It's very sad. A couple of families are going to have their new year completely ruined which is just terrible," Gaskin said.
"The thrill of climbing, it's all part of it. People can't sit in cotton wool all their lives, you take risks and sometimes unfortunately you fail."
There have now been four deaths in Aoraki/Mt Cook National Park in about five weeks.
On December 23, Australian woman Nicola Anne Andrews, 29, died while climbing The Footstool, a 2764m mountain north of Aoraki/Mt Cook, when she fell 300m.
Stephen Dowall, 52, went missing on November 26 after going climbing with a friend.
The pair had left Mt Cook Village about 4am that day, intending to reach the Empress Hut at the head of the Hooker Glacier. But they became separated in the afternoon and Mr Dowall failed to reach the hut.
At least 240 people have died climbing Mt Cook, and dozens of bodies have never been recovered.
