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.
Sergeant Mark Kirkwood of West Coast Search and Rescue said. said police extended their condolences to Ms Simpson's family "at this tragic time".
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.
Sgt Kirkwood said in a statement that police extended their condolences to Ms Simpson's family "at this tragic time".
"The family are understandably grieving and they have asked media to respect their request for privacy during this difficult time," he said.
"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."