He played the obnoxious, poetry-writing anarchist Rick in The Young Ones alongside his friend Adrian Edmondson. The duo later went on to star in the sitcom Bottom.
A pioneer of the 1980s alternative comedy scene, Mayall also appeared in Blackadder and The New Statesman.
His manager Roger Davidson said: "It is a terrible shock. All we know at this stage is that Rik died at home.
"He touched many lives, and always for the better."
Edmondson added: "There were times when Rik and I were writing together when we almost died laughing.
They were some of the most carefree stupid days I ever had, and I feel privileged to have shared them with him.
"And now he's died for real. Without me. Selfish bastard."