Jarman played 19 Tests between 1959 to 1969 and captained Australia for a one match on the 1968 Ashes tour in England when regular skipper Bill Lawry was injured.
“We are deeply saddened to learn of the passing of Barry Jarman, the 33rd captain of the Australian Men’s Test team, aged 84,” Cricket Australia said on Twitter.
“We pass our deepest sympathies to his wife Gaynor and children Kristen, Gavin, Jason and Erin.”
Jarman is one of only five wicketkeepers to have captained Australia’s men’s Test team with Jack Blackham, Billy Murdoch, Adam Gilchrist and Tim Paine being the others.
He worked as an ICC match referee in 25 Tests and 28 one-day internationals between 1995 and 2001 and was awarded the Medal of the Order of Australia in 1997 for service to sport in South Australia.
“Barry was one of South Australia’s internationally known names. He was a great competitor and gentleman, who appreciated the way the game should be played and always had a terrific sense of humour,” South Australian Cricket Association chief Andrew Sinclair said in a statement.
“He lived his life to the full and was not afraid to share his opinion; you were never left in any doubt as to his view. He was a delight to be around.”