It is believed Simpson was hiking down Mt Armstrong in Mt Aspiring National Park when she became disoriented.
She removed her boots and made it into the Pyke Creek water, where she was washed downstream. Her body was found in a canyon at the bottom of the creek.
Creeks in the area usually rose in the afternoons as the glaciers melted from the sun, creating a stronger current, Kirkwood said.
Searchers had found items thought to belong to Simpson in the area before her body was discovered, including a pack and boots, Kirkwood said.
A man in a helicopter spotted the pack from the air, which was confirmed by a review of drone footage from the previous day.
Simpson’s body was found in “close proximity” to the pack, Kirkwood said.
He urged people hiking alone to carry a locator beacon or an in-reach device, which tracked a person’s location in real-time.
He said the family were “understandably grieving” and asked for privacy.
Police extended their condolences to her family at this tragic time, he said.
Police thanked everyone involved in the search since it began on Monday.
“The search was extremely challenging at times, especially in consideration of the terrain, and the work of all involved is to be commended,” Kirkwood said.
The death would be referred to the Coroner.
Last week, torrential rain struck the area and caused slips and flooding throughout Southland and Fiordland.
Simpson’s brother-in-law, Sam Hazelton, previously told Sky News the last time the family heard from her was on the family WhatsApp group early on Thursday morning last week.
“She contacted her friends after that on the Friday to say she was going hiking and camping.
“This was something Stephanie would do most weekends, it was her main reason for staying in Wanaka in New Zealand as it offered so many different trails.”
He said Simpson was “very competent and physically fit”.
“She is relatively experienced in outdoor activities and has already completed a number of hikes. She is such a fun-loving, kind, determined and adventurous woman, we are asking anyone who might know anything to please get in touch with police.”
Simpson, from Essex, was on a working holiday in New Zealand and had been based in Wanaka.