Police confirmed the body was found during an aerial search, and search and rescue teams are now on their way to the site.
Darren Myers, missing since June 1, has been found dead at the bottom of a six-metre waterfall.
It is expected to take some time for the teams to reach the location.
"It happened very suddenly".
"I don't think he suffered at all", he said.
Mr Myers last sent a text message to his family on 30 May - they say they are devastated by the discovery.
According to his Facebook page, Mr Myers was originally from Sawbridgeworth in Hertfordshire, England.
"To know that he's not been able to respond for the last few days is actually a really good relief for us".
Mr Myers is a resident of New Zealand's capital Wellington.
At the time he went missing the ranges were hit by bad weather and snow.
On Monday, police had found a chocolate bar wrapper almost 2,000 feet below where Mr Myers was last known to be.
Sergeant Anthony Harmer had admitted yesterday that the chance was "diminishing" that Mr Myers was still alive.
Myers' disappearance this month prompted warnings about the scenic mountain range, with experts saying shifting conditions - particularly in winter - and challenging terrain made it a danger for even experienced hikers.