Gadsby was one of New Zealand's iconic characters and part of the fabric of New Zealand's culture, the family said.
"His different personas and characters that he played during his television career reflect the Kiwi culture of the time and his humour never dated.
"Jon loved to tell stories and always had a yarn to share around the family table and his quick wit meant many a meal was filled with laughter. And even more so when Jon got his guitars out for a sing-along."
Gadsby had two children, David and Emma, who were "very special to him".
"He took great pride in the young adults they have become and in their achievements," the statement said.
The family also praised the outstanding care he received since his cancer diagnosis, from family and friends, the medical profession and Nurse Maude Hospice in Christchurch.
Funeral arrangements were currently being organised by the family, the statement said, and while details were still to be finalised it was likely to be held on Thursday.
"The family would appreciate some time to grieve in private over the coming days."