Moss was born in London, son of Alfred Moss, a dentist of Bray, Berkshire, and Aileen (nee Craufurd). He was brought up at Long White Cloud house on the right bank of the River Thames. His father was an amateur racing driver who had placed 16th at the 1924 Indianapolis 500. Stirling was a gifted horse rider as was his younger sister, Pat Moss, who became a successful rally driver and married Erik Carlsson.

During his driving career, Moss was one of the most recognised celebrities in Britain, leading to many media appearances. In March 1958, Moss was a guest challenger on the TV panel show What's My Line? (episode with Anita Ekberg). In 1959 he was the subject of the TV programme This Is Your Life. On June 12 the following year he was interviewed by John Freeman on Face to Face; Freeman later said that he had thought before the interview that Moss was a playboy, but in their meeting he showed "cold, precise, clinical judgement... a man who could live so close to the edge of death and danger, and trust entirely to his own judgement. This appealed to me". Moss also appeared as himself in the 1964 film The Beauty Jungle, and was one of several celebrities with cameo appearances in the 1967 version of the James Bond film Casino Royale. He played Evelyn Tremble's (Peter Sellers) driver.  For many years during and after his career, the rhetorical phrase "Who do you think you are, Stirling Moss?" was supposedly the standard question all British policemen asked speeding motorists. Moss relates he himself was once stopped for speeding and asked just that; he reports the traffic officer had some difficulty believing him. As related in the book The Life and Times of Private Eye, Moss was the subject of a less than respectful cartoon biography in the magazine Private Eye. The cartoon, drawn by Willie Rushton, showed him continually crashing, having his driving licence revoked and finally "hosting television programmes on subjects he knows nothing about". It also made reference to the amnesia Moss suffered from as a result of head injuries sustained in the crash at Goodwood in 1962. According to the book, Moss responded by offering to buy the original of the cartoon, an outcome the book describes as "depressingly common" for its satirical cartoons about famous people.  Moss is the narrator of the popular children's series Roary the Racing Car which stars Peter Kay, a role he took on, having been approached by both David Jenkins, who had the original idea, and Keith Chapman, the latter the creator of Bob the Builder, as he saw the TV show as a way of introducing motorsport to the next generation.  He is one of the few drivers of his era to create a brand from his name for licensing purposes, which was launched when his website was revamped in 2009 with improved content. Moss is also a supporter of the UK Independence Party.

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