Booth, whose cause of death was not disclosed, also represented Australia in field hockey at the 1956 Melbourne Olympics.
A middle-order batter, Booth made a century in his first home Test against England in 1962 before scoring another in the next match at the Melbourne Cricket Ground.
“Brian was immensely respected and admired throughout the cricketing community and beyond and we extend our deepest condolences to his wife Judy and their family and friends,” Cricket Australia chief executive Nick Hockley said.