Tidy, known for his appearances on Countdown and the Watercolour Challenge, was awarded an MBE in 2000 for his services to journalism.
His death was announced on his Facebook page by his family.
The post said: “It is with huge sadness that I have to share with you the tragic news that we lost our dad who is not only the most brilliant cartoonist (and) the very best dad two sons, a son in law and a daughter could ever wish for.”
Tidy was born in Liverpool in 1933, the BBC reported.
He did not receive any formal artistic training, instead working for the Royal Engineers in the Army before becoming a cartoonist.
His career began when he sold a sketch to a Japanese newspaper in 1955.
Among his cartoons included The Cloggies, which appeared in the Private Eye from 1967 to 1981, and The Fosdyke Saga, which ran in the Daily Mirror from 1971 to 1985.
The Fosdyke Saga was so popular that it was even made into a BBC radio drama.