Former Wallabies skipper Shehadie represented his county on 114 occasions and took part in 30 Tests, before assuming the Australian Rugby Union (ARU) presidency in 1980 and acting as a driving force behind the inaugural World Cup.
He was inducted into the World Rugby Hall of Fame in 2011 in recognition of his impact on the sport, both on and off the field.
"Today we mourn the loss of a great player, a great leader and visionary and a true gentleman, whose legacy to rugby fans around the world is the Rugby World Cup," a statement from World Rugby chairman Bill Beaumont read.
"Sir Nicholas was an outstanding administrator, whose passion and determination was the driving force behind his enormous contribution to the global and domestic game at what was a pivotal time for the sport.
"The thoughts of the global rugby family are with his family, friends and the Australian rugby community at this difficult time."
Rugby Australia chairman Cameron Clyne said: "Not only have we lost one of our great Wallaby captains, we have lost a truly great Australian. His was an extraordinary life.
"Sir Nicholas is one of the most revered figures in our game across the globe. He was a born leader, a gifted athlete, and an outstanding administrator who was instrumental in shaping the game both nationally and internationally through his various roles in rugby.
"He was the first player to play over 100 matches for Australia, including 30 Test matches, but he was a man that transcended the game and is admired equally for his career in public life following his twelve years of international rugby."