He also captained England in the 1980s, defeating India in 1982 but losing the 1982-83 Ashes series in Australia before announcing his retirement in 1984.
However, he is arguably best remembered for his 8/43 in the second Australia innings of the famous Headingley Test in the 1981 Ashes, when England emerged with an unlikely win from a perilous position thanks to his heroics and those of his new-ball partner Botham.
Since retirement, he has embarked on a broadcasting career with Sky Sports, first as a commentator, then primarily as a pundit.
Willis' family said in a statement: "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."
The Willis family has asked for donations to be made to Prostate Cancer UK.