Former Test captain Simpson was credited with engineering a major turnaround in the Australian team's fortunes during his decade-long tenure as its coach from 1985-86 to 1996.
Under Simpson's coaching, the previously struggling Australian team won four consecutive Ashes (1989, 1990-91, 1993, 1994-95) and ended the West Indies' 15-year unbeaten run in Test cricket in 1995, in their own backyard.
His illustrious playing career included 62 Tests and two ODIs for Australia from 1957 to 1978.
His 4869 Test runs included 10 centuries and 27 half-centuries, with his highest score of 311 against England in the fourth Ashes Test of the 1964 series at Old Trafford.
With his leg-spin bowling, Simpson captured 71 wickets, including a career-best five for 57 against England in the 1963-64 Ashes in Sydney.
Named Wisden Cricketer of the Year in 1965, he retired in January 1968 but returned at age 41 in December 1977 to lead Australia in the home series against India and away series against the West Indies.
"It is a huge honour for me to be inducted into the ICC Cricket Hall of Fame," said Simpson.
"To be inducted in the elite group in Sydney, which I consider the headquarters of Australia cricket, and in front of the people I have known or who have seen me play or been associated with the game here, will make it perfect."
Simpson, 77, will be inducted at a Hall of Fame ceremony on Thursday, joining countrymen Richie Benaud, Allan Border, Don Bradman, Greg Chappell, Ian Chappell, Neil Harvey, Dennis Lillee, Ray Lindwall, Rodney Marsh, Keith Miller, Bill O'Reilly, Steve Waugh, Victor Trumper, Clarrie Grimmett, Frederick Spofforth, Alan Davidson, Glenn McGrath, Shane Warne and Adam Gilchrist.