Cricket officials said Gilmour battled health problems for several years and complications escalated after a recent fall.
The left-armed Gilmour took figures of 6-14 against England in the 1975 World Cup semifinal. The then 23-year-old also claimed 5-48 in the final, which Australia lost to the West Indies.
Gilmour underwent a liver transplant in 2005, when his former captain Ian Chappell led a number of former teammates in raising money for the operation.
