The alarm was raised on Monday and rescue crews watched his beacon moving around the mountain for days as concerns grew.
Lt Harch is an experienced mountaineer and previously scaled Mount Cook for military charity Soldier On, which described him on Friday as an "extraordinary Australian".
Harch parked his vehicle last Friday to climb the mountain and was expected back on Monday, authorities say.
Helicopter pilot Sean Mullally said initial missions up the mountain did not detect any sign of Terry Harch and it was not until the fourth sweep that they saw his waving arm.
They had warm clothing, tents and food to look after him for the night.
"It's a great result, as we did not want the climber spending another night on the mountain", Neville Blakemore, an official of New Zealand's Rescue Coordination Centre, said in a statement.
The man was in "good spirits" given the circumstances, Roberts said.
It was not possible for the team and Harch to walk out of the area on Thursday because of the avalanche risk, he said.
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"That's helped him with his survivability over the last few days".
The Australian Defence Force told News Corp the climber is an Australian Army soldier on leave in New Zealand.
Wanaka Land Search and Rescue spokesman Phil Melchior said Harch had done very well to survive.
"We give all due high praise to the Wanaka Alpine Rescue crew and helicopter crews and police; they've been just wonderful". There were 10km/h southeast winds which were expected to rise to 30km/h in the middle of the day.
The wind chill is minus 16 degrees and snowfall has reached 1200m where the man is stranded, 2300m up the mountain.
Mountain Safety Council chief executive Mike Daisley said he was relieved Harch had narrowly avoided death.
Erik Monasterio, a forensic psychiatrist and mountaineer, earlier said rapidly changing weather patterns made New Zealand's national parks more unpredictable than those in Europe, the United States and Latin America.
Mr Daisley warned mountaineering is a "high risk activity" that requires a certain amount of "common sense" to plan, particularly if you are trekking alone. "It would have been a bloody scary situation to be in".