"Today we were saddened by the news that the search teams found the body of our beautiful girl Nic," the statement read.
"We are so grateful for everyone's support and the hard work that went into the search effort. As a family unit we are devastated, but we are strong and we can get through this together.
Nic Hedley went missing in Dunedin.
"We ask for privacy at this time of sadness so we can deal with our loss."
Up to 60 volunteers joined the search for Hedley, including Coast Guard, Land Search and Rescue teams from North Otago, Catlins and Balclutha, along with specialist search and rescue dogs.
Police also thanked the local Otakou Marae which was used as a base to feed and support those searching for Hedley.