Milligan was born in Ahmednagar, India, on 16 April 1918, the son of an Irish-born father, Captain Leo Alphonso Milligan, MSM, RA, who was serving in the British Indian Army. His mother, Florence Mary Winifred Kettleband, was born in England. He spent his childhood in Poona (India) and later in Rangoon (Yangon), capital of Burma (Myanmar). He was educated at the Convent of Jesus and Mary, Poona, and St Paul's Christian Brothers, de la Salle, Rangoon.
He lived most of his life in England and served in the British Army, in the Royal Artillery during World War II.
Milligan also wrote verse, considered to be within the genre of literary nonsense. His poetry has been described by comedian Stephen Fry as "absolutely immortal - greatly in the tradition of Lear". His most famous poem, On the Ning Nang Nong, was voted the UK's favourite comic poem in 1998 in a nationwide poll, ahead of other nonsense poets including Lewis Carroll and Edward Lear. This nonsense verse, set to music, became a favourite Australia-wide, performed week after week by the ABC children's programme Playschool. Milligan included it on his album No One's Gonna Change Our World in 1969 to aid the World Wildlife Fund. In December 2007 it was reported that, according to OFSTED, it is amongst the ten most commonly taught poems in primary schools in the UK.
While depressed, Milligan wrote serious poetry. He also wrote a novel Puckoon, parodying the style of Dylan Thomas, and a very successful series of war memoirs, including Adolf Hitler: My Part in His Downfall (1971), "Rommel?" "Gunner Who?": A Confrontation in the Desert (1974), Monty: His Part in My Victory (1976) and Mussolini: His Part in My Downfall (1978). Milligan's seven volumes of memoirs cover the years from 1939 to 1950 (his call-up, war service, first breakdown, time spent entertaining in Italy, and return to the UK).
He wrote comedy songs, including "Purple Aeroplane", which was a parody of The Beatles' song "Yellow Submarine". Glimpses of his bouts with depression, which led to the nervous breakdowns, can be found in his serious poetry, which is compiled in Open Heart University.
Even late in life, Milligan's black humour had not deserted him. After the death of friend Harry Secombe from cancer, he said, "I'm glad he died before me, because I didn't want him to sing at my funeral." A recording of Secombe singing was played at Milligan's memorial service. He also wrote his own obituary, in which he stated repeatedly that he "wrote the Goon show and died".
Milligan died from liver disease, at the age of 83, on 27 February 2002, at his home in Rye, East Sussex. On the day of his funeral, 8 March 2002, his coffin was carried to St Thomas's Church in Winchelsea, Sussex, and was draped in the flag of the Republic of Ireland. He had once quipped that he wanted his headstone to bear the words "I told you I was ill." He was buried at St Thomas's Church cemetery in Winchelsea, East Sussex, but the Chichester Diocese refused to allow this epitaph. A compromise was reached with the Irish translation, "Dúirt mé leat go raibh mé breoite", and additionally in English, "Love, light, peace".