Morris was educated at Dauntsey's School, an independent school in West Lavington, Wiltshire. After military service, he attended the University of Birmingham where he graduated in 1951 with a First Class Honours Degree in Zoology. In 1954, he was awarded a D.Phil. from Oxford University for his thesis on the Reproductive Behaviour of the Ten-spined Stickleback, supervised by Nobel Laureate Niko Tinbergen. He was employed by the Zoological Society of London as Curator of Mammals at the London Zoo, eventually leaving in 1966 in frustration about stagnation at the zoo.

Morris first came to public attention in the 1950s as a presenter of the ITV television programme Zoo Time, but achieved worldwide fame in 1967 with his book The Naked Ape. The book is an unabashed look at the human species, notable for its focus on humanity's animal-like qualities and our similarity with apes, and for explaining human behaviour as largely evolved to meet the challenges of prehistoric life as a hunter-gatherer. Reprinted many times and in many languages, it continues to be a best-seller.

His later studies, books and television shows have continued this focus on human behaviour, explained from a bluntly zoological point of view. This approach itself, and his specific conclusions, have often attracted controversy. His book The Soccer Tribe published in 1981 was partly based on research carried out during his directorship of Oxford United, including as it did analysis of the 'tribal' chanting of the club's fans during matches at the club's Manor Ground.

In addition to his scientific pursuits, he is a surrealist artist. His work has been exhibited alongside works by Spanish painter Joan Miró and contributed significantly to the British Surrealist movement. He had his first solo show in 1948, and has shown regularly since then. In 1957, he curated an exhibition of chimpanzee paintings and drawings at the Institute of Contemporary Arts, London, including paintings by a young chimpanzee called Congo. Details from various of Morris's paintings can be seen on the cover art of early editions of Richard Dawkins's books The Selfish Gene and The Blind Watchmaker.

Morris was the executive director of the Institute of Contemporary Arts, London from 1967-68.

Morris oversaw the creation of the gestural and body language for the Paleolithic human characters in the 1981 film Quest for Fire.