Simpson, a landscape gardener in nearby Wanaka, had failed to turn up to work on Monday morning.
Search teams had earlier found items in the area thought to belong to Simpson, including a pack and a pair of boots.
They found her body at 1.40 p.m. local time on Friday, police said.
“The search was extremely challenging at times, especially in consideration of the terrain, and the work of all involved is to be commended,” Mark Kirkwood, the officer in charge at West Coast Search and Rescue, said in a statement.
Mount Aspiring National Park hosts a sizable mountain range, with the highest point rising to nearly 10,000 feet.
“Police would also like to thank everyone involved in the search since it began on Monday for their considerable efforts to locate Stephanie,” he said.