Aiden Webb, 22, from Norwich, had set off to climb the Fanispan mountain on his own on Friday.
His body was found by rangers in Sin Chai village at 12:50 local time (06:50 BST), the head of the Hoang Lien National Park told the BBC.
Mr Webb had fallen and hurt himself on Friday, but his phone stopped working the next day, his girlfriend had said.
Live: Latest on the discovery of Aiden Webb's body
Mr Webb, an experienced climber, had started his ascent of the 3,100m (10,300ft) high mountain - Vietnam's tallest - at about 06:00.
He has been travelling with his girlfriend Bluebell Baughan, 24, of White Notley, Essex, and she was in contact with him by phone from the nearest township of Sa Pa.
She said he had fallen into a ravine and injured his arm and leg and they had agreed that she should call for a rescue team.
The couple last spoke in the early hours of Saturday before his phone stopped working.
Nguyen Quang Vinh, head of the Hoang Lien National Park in Lao Cai province in the north-west of the country, said: "It is very sad that we found the British tourist body today at 12:50.
"The position is quite near the location that his girlfriend gave us, in Sin Chai Village."
His father Trever Webb arrived in Vietnam on Tuesday to join the search for his son.
A British backpacker has been found dead in northern Vietnam, nearly a week after he was last seen.