Mayall shot to fame playing obnoxious, poetry-writing Rick in the 1980s comedy series before enjoying similar success in Blackadder, Bottom and The New Statesman - in which he played scheming Tory MP Alan B'Stard.
The star's Scottish wife, make-up artist Barbara Robbin, found the father-of-three dead at home in Barnes, London, yesterday morning. His death is not being treated by police as suspicious.
Edmondson, who played Vyvyan in The Young Ones, which the pair co-scripted, said: "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."
Impressionist Rory Bremner said: "Oh no. Awful news about Rik Mayall - a fireball of creative comic energy and inspiration. Such brilliant raw talent."
Monty Python star Eric Idle said: "Very sad to hear of the passing of Rik Mayall. Far too young. A very funny and talented man."
Britain's Got Talent judge David Walliams added: "I am heartbroken that my comedy idol growing up, Rik Mayall, has died. He made me want to be a comedian."
Blackadder producer John Lloyd said Mr Mayall, who began his career at London's Comedy Store, was an "extraordinary" person.
He added: "It's really a dreadful piece of news. I remember going to the very first night of the Comedy Store and thinking 'Where does this come from?'.
"It was the most extraordinary thing, him and Ade Edmondson doing the Dangerous Brothers, they were called, and you just felt you were in the presence of something, a whole revolutionary thing."
Mayall was left in a coma for several days after falling from a quad bike in April 1998.