Search coordinator Constable Dave Cogger said Mr Wyatt had an "unsurvivable fall'' from Lake Constance Bluff.
Police were now trying to arrange a formal identification of the body.
Mr Wyatt's family in Britain had been advised, Mr Cogger said.
Police would like to acknowledge the efforts of search and rescue volunteers from Nelson, Golden Bay and Marlborough who worked alongside police during the operation.
Mr Wyatt arrived in New Zealand on November 21 with the intention of walking the Te Araroa Trail, which linked tramping routes from Cape Reinga to Bluff.
The last known sighting of him was on December 15 when he left Blue Lake Hut about 6am.
Teams of expert alpine searchers were to be flown into the Nelson Lakes National Park yesterday to begin a ground search for him.
Bad weather had prevented searchers getting to the area before then, Mr Cogger said.
