He is survived by Lady Elisabeth, son James, daughters Kristen and Susan and five grandchildren.
In a statement, the family remembered one of his favourite comments was that he didn't regret a single day in his life.
"Our father led a rich life filled to the brim with family, sport, business and the community. While he leaves a very big gap in our lives, we are blessed with many wonderful memories of him."
All Black flanker Waka Nathan, who played with Sir Wilson and toured with him to Britain in 1963, said he was a wonderful man and the epitome of a leader.
"I respect him terribly so. He is going to be sorely missed."
Last night, Dan Carter tweeted: "RIP Sir Wilson Whineray. Rugby legend."
Prime Minister John Key said it was fitting that his biography was titled A Perfect Gentleman.
"He was the rare breed of a man whose modesty and humility gave no hint of the greatness he had achieved. This is a loss all New Zealand will feel."
Sir Wilson played for the All Blacks 77 times between 1957 and 1965. His games included 32 tests, all but two as captain. He was New Zealand Sportsman of the Year in 1965.
Sir Wilson had an equally successful business career, gaining an MBA from Harvard University before beginning a long career with Alex Harvey Industries/Carter Holt Harvey, where he became deputy managing director, then chairman.
Business associate John Maasland said he was a clear thinker with a steely business mind, but also a man who understood how to deal with people - "just a lovely guy".
One of his greatest pleasures, Mr Maasland said, was being on the Dilworth Trust, which provides education to boys from disadvantaged backgrounds.
Sir Wilson was knighted in 1994 for services to sport and business.