You are not permitted to download, save or email this image. Visit image gallery to purchase the image.
The 32-year-old disappeared in Mt Aspiring National Park, near Makarora, last weekend after telling friends she planned to hike to Brewster Hut and then move on to Blue Pools.
The officer in charge of the search, Sergeant Mark Kirkwood of West Coast, said Simpson's body was found in the Pyke Creek area near Brewster Hut about 1.40pm today.
"Police would also like to thank everyone involved in the search since it began on Monday for their considerable efforts to locate Stephanie," Sgt Kirkwood said.
"The search was extremely challenging at times, especially in consideration of the terrain, and the work of all involved is to be commended."
LandSAR staff, two dog teams, Alpine Cliff Rescue staff from Fox Glacier, and a canyon search and rescue team from Wanaka assisted with the search today.
Simpson, from Essex, was reported missing about 8.45am on Monday, February 10 when she failed to keep an appointment. She had told friends she planned to hike to Brewster Hut and then move on to Blue Pools.
Search and rescue teams scoured rugged terrain, with teams on the ground, dogs, helicopters and drone with thermal imagery.
Earlier today, police narrowed their search to an area near Fantail Falls, south-east of Haast, after finding Simpson's pack and boots.
Brother-in-law Sam Hazelton previously told The New Zealand Herald her family in the United Kingdom were "hoping upon hope" that she would be found.
"You can't imagine, it's pretty awful. Everybody's just hoping. You go to bed thinking: 'What can we do?'"
Simpson was an extremely fit, experienced tramper, her brother-in-law said.
"She's someone that's done triathlons, running races, marathons, she's really sporty and picks up new skills quickly."
Passionate about tramping, Simpson had hiked for many years in the UK, Australia, and recently, New Zealand.
The last time the family heard from her was when she messaged a family WhatsApp group on Thursday morning that she was going tramping for the weekend.
"It was a normal weekend tramp. That's what she's there for, just to make the most of that free time," Hazelton said.
"She has a real interest in exploring in the outdoors in the environment, she loves new challenges and new adventures."
It is believed Simpson headed out to Mt Aspiring National Park after work on Friday, February 7 and was expected to return on Sunday.
She was carrying a day pack and did not take a search and rescue beacon with her.
Police said the death will be referred to the Coroner.