Born Henry Maxwell Dempsey in Stamford, Connecticut, Harrison's first career was as an artist for comic books, and magazine covers. He also edited magazines and wrote for the Flash Gordon newspaper strip. He published his first novel, Deathworld, at age 35 in 1960.

In a later autobiographical introduction to The Stainless Steel Rat (1957) he described being inspired by the sight of a rat in his studio and realising that such vermin would follow humanity to the stars, and so too would criminals. He began writing a comedic take on a criminal evading the police in a far future interstellar civilisation. The story held him past ... "James Bolivar diGriz I arrest you on the charge—" and the character's dropping a safe triggered by an explosive charge. He finished the short story, later the first chapter of his 1961 novel. Three of the series were later adapted in 2000 AD with art by Carlos Ezquerra.

Harrison continued to write satirical science fiction such as Bill The Galactic Hero (1965) and Star Smashers of the Galaxy Rangers (1973) but also wrote straight detective fiction with Montezuma's Revenge (1972) and ventured in criticism with Great Balls of Fire (1977).

In the 1970s Harrison turned to editing science fiction anthologies, forming a loose partnership with Brian Aldiss, with whom he wrote Hell's Cartographers: Some Personal Histories of Science Fiction Writers (1975).

Harrison's 1966 novel Make Room! Make Room! was filmed as Soylent Green in 1973, with the plot changed from a murder mystery in an overcrowded near future of 1999
to a thriller involving the cover up of the source of the title food stuff in 2022.

Harrison was a renown traveller, living all over Europe and in Mexico. He enjoyed a residency in Ireland and tax free status as an author until his wife Joan died in 2002, when he returned to England. His official site posted his death on 15 August 2012.