Mr Rust, who was a familiar face on the region’s TV screens, passed away on Friday at hospital in Doncaster.
ITV Calendar producer Mark Witty announced his death on Twitter this evening, describing it as ‘very sad news’ and adding ‘all our thoughts are with his family’.
People have been quick to pay tribute.
Fellow forecaster Paul Hudson, with whom he co-wrote the book Weather or Not!, wrote: “Very sad to hear former Yorkshire TV legend weatherman, colleague and co-author Bob Rust has passed away.”
Mike Wood said: “Very sad to hear this. He was a great character.”
ITV Calendar paid tribute to Mr Rust online and said that he never stopped smiling.
It said: "Bob Rust was Calendar's weather presenter for 13 years, retiring in 1996 - and he never stopped smiling.
"The popular weatherman had an army of fans who loved his sense of fun and identified with his humour - particularly when it came to his revolving weather cube. Which didn't always work!"