The ex-opening batsman played 27 Test matches for his country and 495 first-class games for Nottinghamshire between 1940 and 1960.
"Reg Simpson was an elegant opening batsman who served his country with distinction both as a pilot in the Second World War and as a fearless player of fast bowling," BBC Sport quotes England and Wales Cricket Board chief executive David Collier as saying.
"He held a deep passion for the game and for his beloved Trent Bridge. On behalf of everyone at ECB we extend our deepest sympathy to Reg's family."
Simpson scored an unbeaten 156 in the fifth Ashes Test in 1951 to help England win the series against Australia.