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One of the climbers raised the alarm with police on Tuesday night saying the other had fallen.
The bodies of the two climbers were found just after midnight.
Attempts to recover the bodies yesterday were unsuccessful because of poor conditions.
The Taranaki Rescue Helicopter with police search and rescue and Alpine Cliff Rescue crew have returned to the mountain today in an attempt to retrieve the bodies and return them to their families.
The men lived in Christchurch and had travelled to Taranaki as part of their work for environmental and engineering consultancy company Tonkin + Taylor.
They were climbing the mountain in their own time, according to Stuff.
Tonkin + Taylor managing director Dr Tim Fisher said police told the company yesterday morning that two of their "treasured staff" had been involved in a climbing accident.
"Our priority right now is to support their families and our people as we deal with this incredibly sad news.
"We would like to thank Taranaki police and search and rescue for their service and support," a statement provided to Stuff said.
South Taranaki iwi Ngāruahine posted on Facebook that the men climbed up the summit track from the north but have fallen on the southern side of the summit.
A rāhui is in place on the mountain and will be reviewed a week after the bodies are recovered.
It is understood the accident happened near Syme Hut.
Just two weeks ago Tonkin + Taylor posted a tribute on social media from Phillips for well-respected rope technician Tom Arnold after he died in a rockfall near Lake Manapōuri in Fiordland.
He praised Arnold's professionalism and safety-first attitude.