Gosper, who served two stints as International Olympic Committee vice-president and was twice elected to its executive board, passed away after a short illness.
"Kevan was one of the true giants of the Olympic movement, not just in Australia but globally," said Australian Olympic Committee president Ian Chesterman.
"His loss will be felt enormously by so many of his friends who are gathering in Paris for the Olympic Games.
"There will be so many there from across the world who will have a heavy heart today with the news of Kevan's passing."
Gosper was a two-time Olympic runner, competing in Melbourne in 1956 and in Rome in 1960, who went on to forge a distinguished career as a sports administrator.
He was president of the Australian Olympic Committee between 1985 and 1990 before rising to a prominent role within the IOC, serving as an IOC member for 36 years.