"Regarded as one of the great All Blacks legends, Sir Wilson also made significant contributions to the community through his work with sport, charities and business.
"We extend our condolences to Lady Elisabeth and to their family as they remember a much-loved husband, a father and a grandfather,'' Eagle said.
In 2003, he was named patron of the New Zealand Rugby Union and, four years later, he became just the fourth person to be inducted into the IRB Hall of Fame.
Sir Wilson is survived by Lady Elisabeth, one son, two daughters and five grandchildren.
In a statement, his family thanked the staff at Auckland Hospital's critical care unit for their outstanding professionalism and care of duty while looking after their husband and father.
"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.
"We will always remember his energy and passion for everything he did and we remember one of his favourite comments was that he didn't regret a single day in his life.''
Prime Minister John Key paid tribute to Sir Wilson.
"Sir Wilson was a great All Black and may have been the greatest captain we ever had,'' Mr Key said.
"His business acumen was hugely respected as well. He made his mark at APN, the NZ Wool Marketing Corporation, National Bank and Auckland International Airport, although most of us remember his time at the helm of Carter Holt Harvey.
"It is fitting that the only biography of Sir Wilson was titled `A Perfect Gentleman'. He was the rare breed of man whose modesty and humility gave no hint of the greatness he had achieved.
"I knew Sir Wilson and respected him immensely. This is a loss all of New Zealand will feel.''
Sir Wilson was 21 when he made his All Blacks test debut in May 1957 against Australia in Sydney.
He was quickly elevated to the All Blacks captaincy for the 1958 Series against Australia. He was just 23 and, for a long time, he was the youngest All Blacks captain.
Sir Wilson played 77 times for the All Blacks, including 32 tests, and he captained the side 67 times - a massive number of appearances considering the All Blacks played only two or three test matches a year.
His colossal career included being named New Zealand sportsman of the year in 1965.
The following year he won a Harkness Scholarship to Harvard University where he studied for an MBA in 1967 and 1968.
He received his knighthood in 1998 when he was made a Knight Companion of the New Zealand Order of Merit for his services to sport and business.
In the early 1990s he was appointed the Colonel-Commandant of the New Zealand SAS Regiment - a position he held for five years, and one of which he was very proud.
