He had been suffering from cancer.
Sir Brian's wife, Lady Pam, and the couple's three children said they were mourning, but were relieved his suffering had ended. They wanted to express their gratitude for the care and support the family has received since Sir Brian's diagnosis.
New Zealand Rugby chief executive Steve Tew said Sir Brian passed away surrounded by family.
"We have lost a genuine legend of our country, an unwavering figure on the field, and a highly respected figure off it," Mr Tew said.