Darren Myers, 49, went missing while trekking in Tararua Range in the country’s North Island.
An 11-day search ended on Wednesday when a rescue helicopter spotted a body at the bottom of a remote waterfall.
Mr Myers’ brother-in-law said waiting for news had been “the hardest time of our lives”.
Duncan Styles said it came as a relief that he appeared to have died suddenly, rather than waiting in pain.
Speaking to Radio New Zealand, Duncan Styles said: “One of the hardest things we’ve had to bear with, was thinking he’s up there, and alive, and waving at a helicopter, potentially, and not being seen, and being in pain and distress.
“To know that he’s not been able to respond for the last few days is actually really good relief”.
Mr Myers’ wife, Kim, is too upset to speak about it, he said.
Mr Myers, who had recently moved to New Zealand from the UK, had been hiking the Tararua Northern Crossing, a popular trek that can take up to five days.
He sent a text to his wife on 30 May – police now believe he died later that day.
Police search and rescue incident controller Sergeant Tony Matheson said the weather conditions were particularly bad, with wind gusts of up to 145km/h, very poor visibility and rain.
“It happened very suddenly. I don’t think he suffered at all,” he told Radio New Zealand.
“The conditions were just about as bad as you can get up there,” he added.
‘Keen on the outdoors’
Mr Myers was described by his brother-in-law, Mr Styles, as a ambitious man who enjoyed exploring the outdoors.
“Having recently migrated to New Zealand, he wanted to see some of New Zealand’s beautiful countryside – that’s what he was doing,” he said.
“He was used to New Zealand’s weather conditions, and was well aware of what could happen in those environments.”