Elliott was born in London, the son of Nina (née Mitchell) and Myles Laymen Farr Elliott, a barrister. He attended Malvern College and trained at the Royal Academy of Dramatic Art in London. He was asked to leave RADA after one term. As Elliott later recalled: “They wrote to my mother and said, ‘Much as we like the little fellow, he’s wasting your money and our time. Take him away!'”  In World War II, he joined the Royal Air Force, training as a sergeant radio operator and gunner and serving with No. 76 Squadron RAF under the command of Leonard Cheshire. On the night of 23/24 September 1942, his Handley Page Halifax DT508 bomber took part in an air raid on the U-boat pens at Flensburg, Germany. The aircraft was hit by flak and subsequently ditched in the North Sea near Sylt, Germany. Elliott and two other crew members survived and he spent the rest of the war in a prisoner of war camp in Silesia. While imprisoned he became involved in amateur dramatics.  After making his film debut in Dear Mr. Prohack (1949), he went on to play a wide range of parts, often ineffectual and occasionally seedy characters, such as the drunken journalist Bayliss in Defence of the Realm, the criminal abortionist in Alfie, and the washed-up film director in The Apprenticeship of Duddy Kravitz. Elliott and Natasha Parry played the main roles in the 1955 television play, The Apollo of Bellac.  Elliott made many television appearances, notably in plays by Dennis Potter, including Follow the Yellow Brick Road (1972), Brimstone and Treacle (1976), and Blade on the Feather (1980). He took over for an ill Michael Aldridge for one season of The Man in Room 17 (1966) and appeared in the series Thriller (1975).

In the 1980s, he won three consecutive British Academy of Film and Television Arts (BAFTA) awards – Best Supporting Actor for Trading Places as Dan Aykroyd’s kindly butler, A Private Function, and Defence of the Realm – as well as an Academy Award nomination for A Room with a View. He also became familiar to a wider audience as the well-meaning but addlepated Dr. Marcus Brody in Raiders of the Lost Ark (1981) and Indiana Jones and the Last Crusade. A photograph of his character appears in Indiana Jones and the Kingdom of the Crystal Skull and a reference is made to Brody’s death. There is also a statue dedicated to Marcus outside of Marshall College, the school Indy teaches. In 1988, Elliott was the Russian mole Povin, around whom the entire plot revolves, in the television miniseries Codename: Kyril.  Having filmed Michael Winner’s The Wicked Lady (1983), Elliott was quoted in a BBC Radio interview as saying that he and Marc Sinden “are the only two British actors I am aware of who have ever worked with Winner more than once and it certainly wasn’t for love. But curiously, I never, ever saw any of the same crew twice.” (Elliott in You Must Be Joking! (1965) and The Wicked Lady and Sinden in The Wicked Lady and Decadence). Elliott had worked with Sinden’s father, Sir Donald Sinden, in the film The Cruel Sea (1953). He co-starred with Katharine Hepburn and Harold Gould in the television film, Mrs. Delafield Wants to Marry (1986) and with Nicole Kidman in Bangkok Hilton (1989).  In 1988, Elliott was appointed a Commander of the Order of the British Empire (CBE) for his services to acting. His career included many stage performances, including with the Royal Shakespeare Company, and a well acclaimed turn as the twin brothers in Jean Anouilh’s Ring Round the Moon. His scene-stealing abilities led Gabriel Byrne, his co-star in Defence of the Realm, to say: “Never act with children, dogs or Denholm Elliott.”  Despite being described by Screenonline as an actor of “versatile understanding and immaculate technique”, Elliott described himself as an instinctive actor and was a critic of Stanislavski’s system of acting, saying: “I mistrust and am rather bored with actors who are of the Stanislavski school who think about detail.”

Privately bisexual, Elliott was married twice; first to actress Virginia McKenna for a few months in 1954, and later, in an open marriage, to American actress Susan Robinson (7 March 1942–12 April 2007), with whom he had two children, Mark and Jennifer. Jennifer committed suicide by hanging in 2003.  Elliott was diagnosed with HIV in 1987 and died of AIDS-related tuberculosis at his home in Santa Eulària des Riu on Ibiza, Spain, on 6 October 1992 at the age of 70. Tributes were paid by actors Sir Donald Sinden and Sir Peter Ustinov, playwright Dennis Potter and former wife Virginia McKenna. Sinden said: “He was one of the finest screen actors and a very special actor at that. He was one of the last stars who was a real gentleman. It is a very sad loss.” Ustinov said: “He was a wonderful actor and a very good friend on the occasions that life brought us together.” Potter commented: “He was a complicated, sensitive and slightly disturbing actor. Not only was he a very accomplished actor, he was a dry, witty and slightly menacing individual. As a man, I always found him very open, very straightforward and very much to the point.” McKenna added: “It is absolutely dreadful, but the person I am thinking of at the moment more than anybody is his wife. It must be terrible for her.” Ismail Merchant described Elliott as “an all-giving person, full of life … He had an affection and feeling for other actors, which is very unusual in our business.”