Ms Osborne (46) was climbing in the area with her partner when she fell about 200m from the northeastern ridge of the 1692m peak, Senior Sergeant Richard McPhail, of Winton, said.
• Police need help identifying second body
Her partner, whose name has not been released, was airlifted from the mountain on Monday.
A four-person alpine cliff recovery team from Queenstown, in conjunction with Southern Lakes Helicopters, removed Ms Osborne's body from what was described as a "precarious position" on the ridge yesterday afternoon.
Queenstown Alpine Cliff Rescue team member Russell Tilsley said good weather conditions and a 65m-long line attached to the helicopter enabled the volunteers to access and recover Ms Osborne's body.
"We have to work closely with the pilot in situations like this", Mr Tilsley said.
Ms Osborne, who had two sons, aged 15 and 20, had taken up climbing only in recent years, but her partner was a very experienced climber, long-time friend Priscilla Gear, of Invercargill, said.
"She was such a positive person; she loved life and lived life to the full."
Ms Osborne was adventurous and had a very positive outlook on life.
"She died doing something she loved."
She was a human resources adviser for the O'Brien Group, at Mosgiel, and was previously a human resources manager at Hillside Engineering.
O'Brien Group business manager Michael Burwood said she was a much loved and valued member of the team.
Her colleagues were shocked and saddened to hear of her death, he said.
Ms Osborne's role was a national one and she also did work for O'Brien's parent company, Laminex Group.
She would be remembered for projects such as getting the majority of the Mosgiel staff to participate in February's Bike Wise Battle, for which she biked 901km during the month.
"She got us off our butts and on to bicycles," Mr Burwood said.
Dunedin City councillor Colin Weatherall, who also works for Laminex, said Ms Osborne was a very energetic woman who managed to motivate many people.
Her website profile said she was educated at Massey University, had 20 years' experience in human relations, was formally qualified as a mediator and was an experienced negotiator.
