He lived in Miami Beach and died after a long illness, the PGA Tour said. It was not immediately known where he died.
Henning, who was born in South Africa, came to the United States to compete in 1954 and played his way onto the PGA Tour in 1966. That year he won the Texas Open and in 1970 he captured the Tallahassee Open.
He joined the Champions Tour in 1984, where he had three victories in his 18 years on the circuit for golfers 50 and over. Henning also had two international victories in the Liberty Mutual Legends of Golf.
'Harold was instrumental to the development and popularity of the Champions Tour in the early days of its growth,' PGA Tour commissioner Tim Finchem said. 'His affability and warm personality generated tremendous good will for the Tour.'
Henning is survived by his wife, Patricia; children Hanley, Hayley and Harley; a sister; and three brothers. Brother Brian 'Bruno' Henning served as the Champions Tour's vice president of competitions.