Born in Benoni, Western Cape, South Africa, Moore moved to Great Britain at the age of sixteen. By 1939, he was working as a camera operator on the wartime drama Sons of the Sea, directed by Maurice Elvey and photographed by Eric Cross BSC. During the Second World War, Moore served in the Royal Air Force and later joined the RAF Film Production Unit, where he further developed his skills as a cinematographer. His wartime service was recognised with the award of the Distinguished Flying Cross (DFC) and the French Croix de Guerre.
Following the war, Moore established himself as a camera operator on a succession of major British productions. His credits included The African Queen (1951), directed by John Huston and photographed by Jack Cardiff BSC; The Red Beret (1953), directed by Terence Young and photographed by John Wilcox BSC; Hell Below Zero (1954), directed by Mark Robson and photographed by John Wilcox BSC; and The Black Knight (1954), directed by Tay Garnett and also photographed by Wilcox.
Moore received his first credit as director of photography on A Prize of Gold (1955), directed by Mark Robson. He subsequently became closely associated with Irving Allen and Albert R. Broccoli's Warwick Films, photographing a number of their productions, including Cockleshell Heroes (1955), directed by José Ferrer; Zarak (1956), directed by Terence Young; No Time to Die (1958), also directed by Young; and Johnny Nobody (1961), directed by Nigel Patrick. He also photographed Warwick's more prestigious 1960 production The Trials of Oscar Wilde, directed by Ken Hughes.
In 1962, Broccoli and director Terence Young selected Moore as cinematographer for the screen adaptation of Ian Fleming's Dr. No. The film launched one of cinema's most enduring franchises, and Moore went on to photograph a further six Bond films. These included From Russia with Love (1963), for which he won both a BAFTA and the British Society of Cinematographers Award for Best Cinematography; Goldfinger (1964), directed by Guy Hamilton; Thunderball (1965), directed by Terence Young; Diamonds Are Forever (1971), directed by Guy Hamilton; and Live and Let Die (1973), also directed by Hamilton. Moore also photographed portions of The Man with the Golden Gun (1974), again directed by Hamilton, but was forced to leave the production because of illness and was replaced by Oswald Morris OBE BSC. Although Moore subsequently recovered, he did not return to the Bond series.
Beyond the Bond films, Moore's career encompassed a remarkable range of productions. His cinematography on Fred Zinnemann's A Man for All Seasons (1966) earned him both the Academy Award and BAFTA Award for Best Cinematography, making him the first South African to win an Academy Award. His other notable credits included The Day of the Triffids (1962), directed by Steve Sekely, with additional uncredited work by Freddie Francis BSC; The Prime of Miss Jean Brodie (1969), directed by Ronald Neame; The Golden Voyage of Sinbad (1973), directed by Gordon Hessler; Orca (1977), directed by Michael Anderson; and Clash of the Titans (1981), directed by Desmond Davis.
Moore's final screen credit was the 1982 television film Charles and Diana: A Royal Love Story, directed by James Goldstone. By the end of his career, he had established himself as one of Britain's most accomplished cinematographers, combining the technical discipline forged during his wartime service with a distinguished body of work spanning adventure, drama, historical epics and some of the most influential films in British and international cinema.