Gibb described Stigwood as a "creative genius with a very quick and dry wit"."I would like to thank Robert for his kindness to me over the years as well as his mentorship to my family. 'Stiggy' you will be missed," Gibb wrote.
Stigwood, who was born in the South Australia town of Port Pirie, worked with a staggering number of groundbreaking acts, both on the Broadway stage and on the pop charts, producing counterculture stage hits Hair and Jesus Christ Superstar.
He produced the groundbreaking film of The Who's rock opera Tommy and Saturday Night Fever, which introduced disco music and a young John Travolta to audiences around the world, while propelling the Bee Gees to global stardom.
But he was most closely associated with his work with fellow Australians the Bee Gees, whom he guided at the height of their fame in the 1970's. Tributes for the towering industry figure poured in on Tuesday.
Broadway musical producer Andrew Lloyd Webber, with whom Stigwood worked on multiple projects, praised him on Twitter.
"Farewell beloved Robert, the great showman who taught me so much. With love, ALW," he wrote.
Webber later posted a photograph of himself with Stigwood and US producer Hal Prince at Evita's opening night in Adelaide in 1980.
-AAP