They said the body had not been formally identified as that of Andrew Wyatt but it was discovered at the foot of a 100-metre precipice that was on the 41-year-old's intended route.
Wyatt, from Cornwall, was last seen on December 15 in the Nelson Lakes National Park embarking on what was supposed to be a one-day hike to pick up supplies.
Poor weather stopped searchers from reaching the remote area until today, when an air force chopper dropped in four specialised alpine rescue crews who made the grim find.