Marsh enjoyed a superb international career with Australia, recording 96 Test appearances and ending with a then-record 355 dismissals.
He made a further 92 appearances in white-ball cricket for his country in a remarkable 14-year long career lasting from 1970 to 1984.
The former wicketkeeper had been in a critical condition after suffering a heart attack in Bundaberg, Queensland, last week, and his unfortunate passing was confirmed on Friday morning in Adelaide.
Marsh's son Paul confirmed the news in a statement: "On behalf of my mother Ros and brothers Dan and Jamie, it is with immense sadness that I advise that my father Rod passed away peacefully early this morning.
"He has been an incredible husband, father and grandfather and we have been so fortunate to have had him in all our lives."
Marsh's final Test appearance came in January 1984, when Australia faced Pakistan in Sydney.
Not only was it Marsh's final outing, but it was also the final game of Greg Chapell and Dennis Lillee.
Marsh was born in 1947 and raised in Perth alongside older brother Graham Marsh, who went on to win 10 victories on the European Tour as a golfer.
But the duo both grew up playing cricket, and both represented Western Australia as schoolboys.
However, Rodney managed to rise through the ranks and make his debut with West Australia against the West Indies in 1968.
Despite being labelled "Iron Gloves" after dropping a number of catches during the 1970/71 Ashes series, Marsh's superb batting earned him his spot in the national team.
He became the first wicketkeeper to make a century for Australia when he hit 118 against Pakistan in 1972, and his glovework improved on the side.
Upon his retirement, Marsh ended with 3,633 runs, three centuries and 16 fifties - all while taking 343 catches and 12 stumpings in 96 tests.
Tributes have continued to pour in this morning, with Australia captain Pat Cummins one of the first to pay his respects.
in a statement released by Cricket Australia, Cummins said: "I, along with countless other people in Australia, grew up hearing the stories of him as a fearless and tough cricketer, but his swashbuckling batting and his brilliance behind the stumps over more than a decade made him one of the all-time greats of our sport, not just in Australia, but globally.
"When I think of Rod, I think of a generous and larger-than-life character who always had a life-loving, positive and relaxed outlook, and his passing leaves a massive void in the Australian cricket community."
The International Cricket Council also commented on Marsh's joyous character outside the field as well as on it, describing him as a "true legend of the game".
The ICC's chief executive Geoff Allardice said, "His legacy has gone way beyond what he achieved on the field," Allardice said.
"An ICC Hall of Fame inductee in 2009, he played a significant role in developing young cricketers all around the world, including through his time as the inaugural director of coaching at the ICC Cricket Academy in Dubai, a facility that future generations of players from all countries will continue to benefit from.
"He will be sorely missed and the thoughts of everyone at the ICC are with his family and friends."