The remains, which date back to 1976, were found by trampers on the "toe end" of Bonar Glacier on March 19.
The trampers contacted police who then alerted Wanaka Search and Rescue.
A two-member alpine rescue team accompanied police officers in retrieving the remains from the glacier.
A police spokesman said they were waiting for the identity of the dead climber to be confirmed before contacting relatives.
Search and Rescue spokesman Bill Day described the procedure as routine.
Police removed the remains from the glacier and the alpine team was in attendance for safety reasons.
Mr Day did not believe climate change was necessarily the reason why the bones had become exposed.
"It is more the fact the glacier is moving... At this time of year there is not as much cover," Mr Day said.
Bonar Glacier was on the route for climbers ascending Mt Aspiring and had a reputation for being a gruelling approach.
