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Searchers recovered her body in the Pyke Creek area about 1.40pm yesterday, Sergeant Mark Kirkwood, of West Coast Search and Rescue, confirmed last night.
Earlier, they had found ‘‘items of interest’’ in the area which were thought to belong to Ms Simpson, including a pack and a pair of boots.
Sgt Kirkwood said police wanted to extend their condolences to Stephanie’s family at what was a ‘‘tragic time’’.
‘‘The family are understandably grieving and they have asked media to respect their request for privacy during this difficult time.
‘‘Police would also like to thank everyone involved in the search since it began on Monday for their considerable efforts to locate Stephanie.
‘‘The search was extremely challenging at times, especially in consideration of the terrain, and the work of all involved is to be commended.’’
The discovery of her body followed a search by Alpine Cliff Rescue staff from Fox Glacier, LandSAR staff, two dog teams, and a canyon search and rescue team from Wanaka.
Ms Simpson’s parents had earlier arrived in New Zealand from the United Kingdom, and were being supported by a police family liaison officer.
The search for Ms Simpson began on Monday morning when she failed to show up to her landscaping job in Wanaka.
She had told friends of weekend plans to attempt the challenging four-hour hike to Brewster Hut and then move on to Blue Pools.
Police said the 32-year-old from Essex, who was believed to have been hiking alone, carried a day pack and probably did not take a search and rescue beacon.
Her brother-in-law, Sam Hazelton, previously told The New Zealand Herald her family had been ‘‘hoping upon hope’’ 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?’’’
She was an extremely fit, experienced tramper, her brother-in-law told the Herald.
‘‘She’s someone that’s done triathlons, running races, marathons, she’s really sporty and picks up new skills quickly.’’
A crowdfunding campaign to support the LandSAR rescue team had also been launched by a friend who described her as ‘‘the most kind-hearted caring person you could wish to know’’.
Meanwhile, friends of Ms Simpson's have been paying tribute to her online.
Close friend Danny Kilbane said: "We are all heartbroken and are going to struggle to come to terms with our loss.
"Steph you will be missed by all more than words can explain. RIP angel."
Bekah Jane, who met Ms Simpson in December when she took on a gardening and landscaping job in Wanaka where they both lived, described her as the sister she'd never had.
Ms Simpson moved to Wanaka three months ago after a stint travelling in Australia.
"Little did I know I was about to meet someone who would become my best friend," Ms Jane wrote on her Facebook tribute.
"We were always together, from doing small things like getting groceries to going out with friends and having girly days just painting our nails and relaxing. It felt like having a sister I've never had."
Ms Jane described Ms Simpson as sparkly and infectious, with a thirst for life.
"Right now my heart is completely shattered. I feel robbed of the many years of friendship ... at the same time I feel overly blessed to have had the time with her that I did."
The death will be referred to the coroner.
- additional reporting NZ Herald