Bland's death was announced by South Africa's Sunshine Tour golf circuit. He died Tuesday "after a battle with cancer" with his family and bulldog named "Handsome" by his side, the Sunshine Tour said.
Bland won 36 titles in all and went head-to-head with the best players in the world in some of his most memorable performances.
For his two European tour victories, he beat out two-time Masters champion Bernhard Langer at the Benson and Hedges International in England in 1983.
In 1986, Bland won the Suze Open in France by four shots from golfing great Seve Ballesteros.
He claimed five wins on the Senior PGA Tour and three on the European Senior Tour, with his last coming in 2010.
Bland lost to nine-time major champion and compatriot Gary Player in a playoff at the 1997 Senior British Open.
The Sunshine Tour said Bland was "one of the most loved and respected South African sportsmen."