Morse's first name, "Endeavour", was kept a secret until the end of Death is Now My Neighbour (traditionally Morse claimed that he should be called "Morse" or joked that his first name was "Inspector"). In the series it is noted that his reticence about his "Christian" name led to a public school (Stamford School, where Colin Dexter and his brother were both pupils) nickname of "Pagan". The origin of his name is the vessel HM Bark Endeavour, as Morse's mother was a Quaker (Quakers have a tradition of "virtue names") and his father was a fan of Captain James Cook. The author of the Morse novels, Colin Dexter, is a fan of cryptic crosswords, and Morse is named after champion solver Jeremy Morse, one of Dexter's arch-rivals as a clue-writer in the crossword world.

During the episode "Cherubim and Seraphim", it is learned that Morse's parents divorced when he was 12. He remained with his mother until her death three years later, when he had to return to his father. He had a dreadful relationship with his stepmother, Gwen, and claimed he only read poetry to annoy her and that her petty bullying almost drove him to suicide. He has a half-sister, Joyce, with whom he is on better terms, and was devastated when Joyce's daughter, Marilyn, took her own life.

Morse is ostensibly the embodiment of white, male, upper-middle-class Englishness, with a set of prejudices and assumptions to match. He may thus be considered a late example of the gentleman detective, a staple of British detective fiction. This background is in sharp juxtaposition to the working class origins of his assistant, Lewis (named for another rival clue-writer, Mrs. B. Lewis); in the novels, Lewis is Welsh, but this was altered to a northern (Geordie) background in the TV series. He is also middle-aged in the books.

Morse's relationships with authority, the establishment, bastions of power and the status quo are markedly ambiguous, as sometimes are his relations with women. Morse is frequently portrayed in the act of patronising women characters, to the extent that some feminist critics have argued that Morse is a misogynist.

Morse is an extremely intelligent individual. He dislikes spelling errors and grammatical mistakes, demonstrated by the fact that in every personal or private document written to him he manages to point out at least one spelling mistake. He claims his approach to crime-solving is deductive and one of his key tenets is that "there is a 50 per cent chance that the last person to see the victim alive was the murderer". In reality, it is the pathologists who deduce; Morse uses immense intuition and his fantastic memory to get to the killer.

Although details of Morse's career are deliberately kept vague, it is hinted that as a schoolboy he won a scholarship to study at St John's College, Oxford. He lost the scholarship as the result of poor academic performance, which in turn resulted from a failed love affair (mentioned in the series at the end of "The Last Enemy" and in the novel The Riddle of the Third Mile). Forced to leave the University, he entered the Army, and on leaving it, joined the police. He often reflects on renowned scholars (such as A. E. Housman) who, like himself, failed to get academic degrees from Oxford.

The novels in the series are:

Inspector Morse also appears in several stories in Dexter's short story collection, Morse's Greatest Mystery and Other Stories (1993, expanded edition 1994).

Dexter killed off Morse in his last book, The Remorseful Day. Morse dies in hospital from complications of his neglected diabetes, a disease Colin Dexter shares.

The Inspector Morse novels were made into a TV series (also called Inspector Morse) for the British TV channel ITV. The series was made by Zenith Productions for Central (a company later acquired by Carlton) and comprises 33 two-hour episodes (100 minutes excluding commercials)—20 more episodes than there are novels—produced between 1987 and 2000. The last episode was adapted from the final novel, The Remorseful Day, which revealed Morse's given name.