David Gower, who succeeded him as England captain, said his former team-mate and commentary colleague had a "burning, bright passion for the game."
"He was a guy that, whenever I had problems in the cricketing world or in my personal life, he was always there to help me," Botham recalled.
"He was like a big brother. There are certain friendships you have in your life but very few as close as it was with Bob.
"An amazing guy, great cricketer, very underestimated by a lot of people for many years. He was the best quick bowler I played with representing England because he was quick. He was a unique bowler, because you would never teach anyone to run up and bowl like that.
"I knew that he was very, very ill. I saw him last Thursday, went down and sat with him for a while, but when it actually happens it's a major shock still. You can't really be prepared for losing such a close, close friend."
''My condolences to his family and loved ones.''
After retiring, Willis embarked on a second career as a cricket commentator.