"This is the best possible outcome we could have hoped for in the circumstances", Detective Sergeant Derek Shaw said.
"We are glad to be able to bring some degree of closure to Matthew's family at this sad time.
"Police would like to thank the Wallis family, New Zealand Defence Force, LandSAR volunteers, the Wanaka community and the aviation industry for their assistance in this recovery operation.
"Matthew's family ask the media to please respect their privacy as they come to terms with their loss."