He said a Westpac Rescue Helicopter was sent to the scene but the man had died.
The helicopter transported the climber's body to Arthurs Pass, where it was expected to be taken back to Christchurch.
It was understood another member of the man's climbing party had raised the alarm, and police were now informing his family.
The death had been referred to the coroner.
Christchurch Westpac Rescue Helicopter crewman Wayne Ledgerwood said it was a harrowing job to attend, and it was on the mountain's north facing Otira Face.
He said the two other members of the man's climbing party -- two women -- were "extremely upset".
"We were sent out to a climbing party, a member of which had fallen out there. Once we located them on the hillside we put a paramedic down and assisted the patient but unfortunately he was deceased at that stage.
"He had fallen approximately 50m when they were descending the mountain."
He said the two women were flown back to Arthurs Pass before the man's body was retrieved.
Mr Ledgerwood said it was the most recent in a spate of climbing-related rescues in the area.
"At the moment it seems to be reasonably common that we are going up into the likes of the Arthurs Pass area to recover climbers who have been hurt."
Mountain Safety Council chief executive Mike Daisley said it was too soon to know the intricate details of what happened this morning, but it was undoubtedly a tragedy.
"It is always a tragedy when people die in the outdoors. Mt Rolleston in particular is a beautiful place for people to visit, but it always a tragedy when someone has an unfortunate accident."
He said that Mt Rolleston was a very steep and unstable terrain, and only climbed by those with a lot of experience.
"I don't know about this climber and their experience but to be in that environment and at that time of day on a Monday morning suggests they had experience.
"That area is known for its very unstable rocks, some people describe it is as like Weet-Bix. It's very steep and can get near vertical in places.
"If you make a small slip, there is a very small margin of error."
In light of the accident, and ahead of Waitangi weekend, Mr Daisley recommended people familiarise themselves with the organisations' safety guidelines.
The death follows a number of others on New Zealand mountains in recent weeks.
Two Australian climbers died on Mt Cook on December 28.
Australian couple Stuart Jason Hollaway, 42, and his partner. Dale Amanda Thistlethwaite, 35, were roped together when they fell during a weeks-long climbing trip in New Zealand.
Also in December, 28-year-old Nicola Andrews died when she fell 300m from the Eugene Glacier in the Aoraki-Mt Cook National Park.