The star, who shot to fame playing poetry-writing anarchist Rick in The Young Ones, was found dead at his home in London on Monday.
Writing on Facebook, Bonnie Mayall said: "My dad was loved not only by my family, but by many many others.
"We will never forget him and neither will the world.
"R.I.P to the man, the myth, the legend - my wonderful, generous, foul-mouthed and hysterical father. My idol now and forever. We love you daddy."
Mayall's Comic Strip Presents... colleague Peter Richardson, whose son was one of the last people to see the actor alive, said he was happy and healthy in the hours before his death.
Richardson, who directed Mayall in a string of hit TV shows, told the BBC Radio 4 Today programme his son saw him around half an hour before he died.
He said: "He was happily chatting away and it was very quick. We still don't quite know what happened, but it was a seizure of some sort."
Mayall, who leaves his wife, Barbara, and three children, Rosie, Sidney and Bonnie, survived a near-fatal quad bike crash in 1998, which left him in a coma for five days.
Richardson said: "He had 16 years after the quad bike [accident] and at the time I don't think people thought he would survive ... it was just shocking that he went - he was so happy and seemed very healthy when he did go."
Richardson said Mayall - who appeared in some of Britain's best-loved shows, including Blackadder and Bottom - "loved playing the bad boy".