Booth played 29 Test matches for Australia, including two as captain. He recorded five Test centuries and was a key player for the Australian team in the early 1960s, scoring 1,773 runs at an average of 42.21.
Booth, whose cause of death was not disclosed, also represented Australia in field hockey at the 1956 Melbourne Olympics.
As a middle order batsman, Booth made a century in his first home Test against England in 1962, and then made another in the next game at the Melbourne Cricket Ground.
Brian was greatly respected and admired throughout the cricket community and beyond, and we extend our deepest sympathy to his wife Judy, their family and friends, said Cricket Australia chief executive Nick Hockley.