"We cannot put into words what it feels like to have David returned to us after all this time but we are taken back to when he first went missing back in 1973.
"David's spirit still remains in the beautiful, peaceful environment which claimed the life of a wonderful and dearly loved young man in the prime of his life."
Canterbury police Area Commander Inspector Dave Gaskin said police would continue to support the family as they came to terms with Mr Moen's remains being returned to them.
Another set of historical remains were found near the Hochstetter Glacier at the start of March this year, but they had not been formally identified, he said.
"We are pleased that we have been able to return David to his immediate family. He was lost in tragic circumstances doing a sport he loved," he said.
The coroner is considering whether a previous inquest into Mr Moen's death should be reopened.