In 133 matches for the All Blacks between 1957 and 1971, the former King Country lock played 55 tests and became recognised throughout the world as the face of New Zealand rugby.
NZR said his wife Verna, Lady Meads and the couple's five children wished "to express their sincere gratitude for the care and support the family has received in the past 12 months"since his diagnosis.
"Our heartfelt thanks to the staff at Te Kuiti Medical Centre, particularly doctors David McLean and Keith Buswell, and to the nursing staff at Te Kuiti Hospital for their superb care of Colin," the family said.
"To our friends, thank you for your love and care.
"The visits and phone calls were enjoyed by Colin and appreciated by us all.
"To those throughout the country who sent Colin best wishes, we thank you for your kindness."
Meads' youngest daughter Shelley Mitchell paid tribute.
"Dad led a full life," she said.
"He loved being an All Black and he loved his family dearly.
"We will miss him terribly."
Sir Colin is survived by Lady Meads and their children Karen, Kelvin, Rhonda, Glynn and Shelley; their 14 grandchildren and seven great grandchildren.
The Meads family has requested privacy at this time.
News of his passing has been met with sadness around the world.
One of the first to pay tribute to Sir Colin was Labour leader Jacinda Ardern.
"RIP Sir Colin Meads. #legend," she tweeted.
Prime Minister Bill English said it was a sad day for New Zealand rugby and for New Zealand.
"I have had the privilege of getting to know Sir Colin. He was not only a great All Black but also a genuinely good New Zealand bloke.
"He represented what it means to be a New Zealander. He was no-nonsense, reliable, hardworking, warm and very generous with his time.
"I remember when I was younger hearing stories about how he used to shear sheep all day and go running at night. I thought I'd give it a go. I quickly learned the Meads legend was built on physical and mental toughness.
"My thoughts are with Sir Colin's wife Lady Verna, and his family and friends at this time."