Milligan: A household name since the 1950s
Prince Charles, one of his ardent fans, said he was "deeply saddened" by his death.
Milligan was one of Britain's most respected performers and was known to millions as one of the founding members of The Goons.
Milligan had been the last surviving member of the quartet.
Prince Charles said: "It was an immense sadness to learn of Spike Milligan's death and my heart goes out to all his family.
"Personally, but along with so many others, I shall miss his irreverent and hysterical presence and can only say that the world really will be the poorer for his departure."
Milligan's agent said he died surrounded by his family.
He is believed to have died from liver failure and had suffered ill-health for sometime.
In recent months had been nursed by his third wife Shelagh.
Comedian Stephen Fry paid tribute to his talent: "Spike was entirely his own mad Irish self. He came out of nowhere.
"If there is a definition of genius it is that whatever province you are in, you leave it different. He left comedy different and it was never the same after him."
Fry described his writings as "absolutely immortal".
He was a major influence on British comedy, taking music hall ideas and weaving into them his own sketches.
His fascination with language and the surreal qualities of everyday life broke new ground in humour and was reflected in both his sketches and popular children's books.
Fantasy
Friend and broadcaster Nicholas Parsons told BBC News 24: "There will never be another Spike. He broke the mould of comedy.
"He took comedy into the world of fantasy; it was surreal and different and amazing. He created a whole new attitude to humour."
BBC director general Greg Dyke said: "Spike Milligan was a comic genius. As the writing brains behind the Goon Show he was the founder of modern comedy."
Comedian Eddie Izzard described him as the "godfather of alternative comedy".
He said: "He was a great man. He was a crazy, wonderful genius."
Broadcaster Michael Parkinson said Milligan was "indisputably the most important in British comedy over the last 50 years".
The BBC's head of comedy, Jon Plowman, added: "It is very sad. He was one of the true greats whose influence can be seen in a huge amount of comedy that we do today."
Breakdown
The Goon Show was first broadcast on 28 May 1951.
Milligan is said to have picked the word goon out of a Popeye comic and started using it as derogatory term for people he saw as idiots.
Milligan was credited with writing the majority of the Goon scripts but during series three he suffered a breakdown and had to miss 12 episodes.
He received an honorary knighthood from Prince Charles last year - Milligan held an Irish passport - despite making fun of him during a live television show in 1994 by calling him "grovelling".
Depression
He later sent a fax to the prince saying: "I suppose a knighthood is out of the question now?"
Plagued with mental illness and manic depression during his life, he suffered no fewer than ten breakdowns, linked to shell shock he endured during the war.
He went on to star in the Q series of television shows and also wrote several books, including Adolf Hitler, My Part In His Downfall.