The former fast bowler, who made his debut in 1971, was a key player for more than a decade and played in 90 Tests and 64 ODIs, before retiring in 1984.
Willis finished a glittering career with 325 Test wickets and 899 first class wickets.
Following retirement he became a popular pundit on Sky Sports, regularly delivering funny lines about the day’s play and damning verdicts on suspect performances.
A Willis family statement read: ”We are heartbroken to lose our beloved Bob, who was an incredible husband, father, brother and grandfather.
“He made a huge impact on everybody he knew and we will miss him terribly.”
England director of cricket Ashley Giles paid tribute to Willis: “Such sad news about Bob Willis, he was a great man.”
Willis played in the same team as Sir Ian Botham, with his hostile spell of bowling (8/43) proving pivotal in the third Test against Australia at Headingly in 1981, which would later become known as the “Botham Ashes”.
Botham would describe Willis as a “tremendous trier, a great team-man and an inspiration – the only world-class fast bowler in my time as an England player.”
Willis is survived by his wife Lauren, daughter Katie, brother David and sister Ann.