Richardson, who directed Mayall in a series of TV shows, said the 56-year-old was "such a star".
He told the BBC Radio 4 Today programme that his son saw him around half an hour before he died at his London home yesterday.
He said: "He was happily chatting away and it was very quick and 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 an almost fatal quad bike accident in 1998 which left him in a coma for several days.
Richardson said: "He had 16 years after the quad bike and at the time I don't think people thought he would survive that but he lived for another 16 years and it was just shocking that he went - he was so happy and seemed very healthy when he did go."
Mayall shot to fame playing poetry-writing anarchist Rick in The Young Ones, and enjoyed a glittering career which saw him appear in Britain's best-loved shows including Blackadder and Bottom.
Richardson said the star "loved playing the bad boy", but was very different in real life.
He said: "He always wanted to be a rebel but in fact was a lovely family man who did the washing up and was just a very warm person and not as selfish and vain as he liked to make out really."
Close friend and long-time collaborator Adrian Edmondson led the tributes to Mayall, saying he felt privileged to have shared "carefree stupid days" with him at Manchester University, where the pair studied.
He 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."
Stephen Fry, who also starred in Blackadder, said on Twitter: "Simply distraught to hear of the death of Rik Mayall. An authentic comedy genius and a prince among men."
Ben Elton, who was also a university friend of Mayall, said: "I owe him so much. He changed my life utterly when he asked me to co-write The Young Ones with him and he was with me on the day I met my wife. He always made me cry with laughter, now he's just made me cry."
Mayall's Young Ones co-star, Nigel Planer, told the BBC he was "very, very sad and upset that we've lost Rik, who was inspirational, bonkers, and a great life force".
He described Mayall as "a brilliant comedian and someone who made everyone else's lives more fun. He will be really, really missed".
Student Rick in The Young Ones - a pompous wannabe anarchist who loved Cliff Richard - was one of Mayall's best-known characters.
Sir Cliff, who in 1986 recorded a charity version of his hit single Living Doll with the show's cast for Comic Relief, paid tribute to Mayall, saying: "I became a fan of his when he was in The Young Ones show and was always thrilled when he used my name during his series.
"I am so sad at his parting."
It is not yet known what caused Mayall's unexpected death and his wife Barbara Robbin - who is understood to have found his body at their home in Barnes, south west London - told the Daily Mirror she had no idea what had caused his death and would have to wait for a coroner's report.
A Scotland Yard spokesman said officers were called by London Ambulance Service to a house in Barnes where "a man, aged in his 50s, was pronounced dead at the scene".
He added that the death was not believed to be suspicious.
Mayall was born in Harlow, Essex, to drama teacher parents and launched his comedy career on stage in a duo, The Dangerous Brothers, with Edmondson.
He also appeared as the swashbuckling Lord Flashheart in Blackadder and played the conniving Conservative MP Alan B'Stard in The New Statesman.