Her body was discovered in the Pyke Creek area of Mount Aspiring National Park, where she went missing several days ago, at about 1.40pm on Friday, Sergeant Mark Kirkwood of West Coast Search and Rescue said.
Searchers had earlier found items thought to belong to Ms Simpson in the Pyke Creek area, including a back pack and a pair of boots.
Sgt Kirkwood said police extended their condolences to Ms Simpson’s family ”at this tragic time”.
He added: “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 death will be referred to the coroner.
Ms Simpson, 32, and originally from the Basildon area of Essex, was reported missing on Monday after she did not turn up to her job as a gardener in the Wanaka area, where she had been living.
She had told friends she had planned to go hiking in Mount Aspiring National Park at the weekend.
A close friend told the New Zealand Herald that her decision to head out into the mountains was just “another weekend” of hiking for Ms Simpson.
“She’s strong, she’s fit, she’s capable. She’s worked in the outdoors, she knows what she’s up to.” she said, adding, “She’s a really beautiful, kind-hearted person.
“She can make friends in an instant, she’s awesome. She’s just here to [hike] and see the country.”
Ms Simpson was the third traveller to have gone missing in the southwest region of New Zealand’s South Island after heavy rain caused rivers to swell and damaged a number of trails.
On Friday, the bodies of two hikers, a man and a woman, were pulled from the Makora river, close to where Ms Simpson was believed to have been walking.
Additional reporting by PA