The 74-year-old, who played 96 Tests and went on to be a longtime national manager, was in an induced coma and died in a hospital in Adelaide.
Marsh made his debut in 1970 before retiring in 1984 with what was then a world record 355 Test layoffs, many thanks to the bowling of legendary paceman Dennis Lillee.
He was the first Australian wicketkeeper to score a Test century.
“It wasn’t just his playing ability, although that was a big part of it,” Chappell said.
“The thing with Rod is you knew where you were at with him, he always said what he thought, and you can handle that, because he was outspoken.”
Confirming his death, Cricket Tasmania said it was “extremely saddened to learn of the passing of Rod Marsh overnight”.
“Rod is an icon of Australian cricket and his passing means a great loss to the game around the world,” he added.
Marsh is survived by his wife Roslyn and sons Daniel, Paul and Jamie.
He had been attending a charity event in the state of Queensland last week when he collapsed, with his son Paul announcing on Monday that his father remained in an induced coma.