The pace bowler played 90 Tests for England and has been a popular figure in broadcasting since his retirement in 1984.
Sky Sports announced news of Bob’s death on Wednesday, with his family releasing a statement to the broadcaster.
“We are heartbroken to lose our beloved Bob, who was an incredible husband, father, brother and grandfather,” they said. “He made a huge impact on everybody he knew and we will miss him terribly.
“The Willis family has asked for privacy at this time to mourn the passing of a wonderful man and requests that in lieu of flowers, donations should be made to Prostate Cancer UK.”
Bob’s most famous moment as a player came in the 1981 Ashes series as his eight for 43 fired England to a remarkable win in the third Test at Headingley.
He is England’s fourth highest wicket-taker of all time with 325 wickets.
Bob’s former county Surrey paid tribute on Twitter, saying: “All at Surrey County Cricket Club are devastated to learn of the passing of former Surrey and England bowler Bob Willis.
“Our thoughts are with his family and friends at this time.”
Former England fast bowler Darren Gough said Bob was “hugely admired”.
“As a player he had a big heart, he’d run in, nearly 6ft 6ins, and hit the pitch hard. At his peak was one of the best three bowlers in the world,” he said on Talksport.
“He was hugely admired all around the world. Everybody knew who he was.
“If you just saw him on TV people might think he’s a bit straight, but in his company over a glass of wine he would make you laugh all night.”
Bob is survived by his wife Lauren, daughter Katie, brother David and sister Ann.