The star, who shot to fame playing Rick in The Young Ones, was 56 and his career included appearances in shows including Blackadder, Bottom and The New Statesman.
He was left seriously ill after a quad bike accident in 1998 which left him in a coma for several days, but was working until recently.
Speaking about the accident last year, Mayall said doctors had kept him alive on a life-support machine for five days and were about to turn it off when he began to show signs of life.
He used to mark the occasion by exchanging presents with his wife and children and said the near-death experience changed his life.
He said: "The main difference between now and before my accident is I'm just very glad to be alive.
"Other people get moody in their forties and fifties - men get the male menopause. I missed the whole thing. I was just really happy."
Mayall started on stage in a duo, The Dangerous Brothers, with long-time collaborator Adrian Edmondson after they met at Manchester University
The pair, who appeared together in The Young Ones, reprised their original act in the anarchic comedy Bottom.
Among those paying tribute to Mayall was David Walliams, who said: "I am heartbroken that my comedy idol growing up, Rik Mayall, has died. He made me want to be a comedian."
Impressionist Rory Bremner said: "Oh no. Awful news about Rik Mayall - a fireball of creative comic energy and inspiration. Such brilliant raw talent."
Blackadder producer John Lloyd said Mayall was "just extraordinary".
Speaking to BBC News, he said: "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."
BBC director of television Danny Cohen said: "Rik Mayall was a truly brilliant comedian.
"His comic timing was outstanding and his screen presence unique. For a generation of viewers he was a true comedy hero."
Mayall's spokeswoman confirmed that the actor, who was married with three children, died at home in London.
Mayall, who was born in Harlow, Essex, to drama teacher parents, also appeared in shows including Filthy, Rich and Catflap.
Other notable characters included the conniving Conservative MP Alan B'Stard in The New Statesman and the feckless investigative journalist Kevin Turvey.
Actress Helen Lederer, who appeared in The Young Ones, tweeted: "Rik Mayall, I loved you. Gutted. The man who taught me not to crash laughs, has crashed. Real love to wife, children. Massive loss."
Comedy star Noel Fielding wrote: "Growing up there was no-one funnier! We will really miss you Rik Mayall you genius."
Trainspotting writer Irvine Welsh wrote: "Rik Mayall spread a lot of fun and laughter. Very sad to see him taken before his time."
Actor David Harewood said: "RIP Rick Mayall. Great comedian and actor. Funny, brilliant and sharp as nails."
A Scotland Yard spokesman said officers were called by London Ambulance Service to a house in Barnes, south-west London at around 1.20pm where "a man, aged in his 50s, was pronounced dead at the scene".
The death is not believed to be suspicious, he added.
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."
Writing on Twitter, Bob Mortimer said: "Last time I saw him he grabbed my crotch and said 'Not eaten yet then?" So sad.. Funniest man of his generation."