The 62-year-old was last seen by family in Tauranga on Saturday and was reported missing the following day.
Her Nissan Tiida was found at the Wairere Falls carpark near Matamata yesterday.
Police said this afternoon her death would be referred to the coroner.
“There are no suspicious circumstances in relation to the death. Police would like to thank the members of the public who provided information which assisted in locating the woman. Police extend our condolences to the family.”
A helicopter was seen in the falls area this afternoon.
Earlier today, a long-time friend of Coxhead’s told the Bay of Plenty Times she was a “wonderful” and “adventurous” person.
They had known each other for about 30 years.
The woman, who asked not to be named, said Coxhead used to be a primary school teacher and taught her daughter and grandson in Tauranga.
She said her friend had two sons.
“Because Jude is such a bubbly, happy outgoing person, everyone on first meeting her just loves Jude.
“She is a very busy person, who is involved in lots of different activities, including volunteering, tramping and walking, and she spends a lot of time outdoors. Jude is quite an adventurous person.”
She said Coxhead decided in the past couple of years she wanted a career change and gave up teaching.
Due to her love of gardening she had been working part-time at a garden centre in Bethlehem.