Born in Liverpool, Lancashire, the son of a publican, Rossington was educated at Sefton Park Elementary School and Liverpool Technical College. He left education at the age of 14. After that he lived a rather aimless adolescent life as messenger, office boy at Liverpool Docks and apprentice joiner. He did his national Service in the RAF. Later, he went to night school and studied industrial design at technical college to become a draughtsman. His interest in acting led him to the David Lewis Theatre, a local theatre group where he began his acting career. Here he played Shakespeare and in The Critic under the direction of Thomas G Reed. Rossington went on to train at the Bristol Old Vic Theatre School city's Theatre Royal, by the mid-1950s appearing on the stage in plays such as a London Old Vic tour of the USA in A Midsummer Night's Dream and Salad Days, being one of the original cast. However, his big breakthrough came in 1957, when he starred as Private 'Cupcake' Cook in the popular sitcom The Army Game. He left after three series in 1959, and in the meantime had appeared in I Only Arsked!, again as 'Cupcake'.

His first film role was in the 1956 film Three Men in a Boat. Rossington went on to appear in Carry On Sergeant, the first Carry On film, as well as Carry On Nurse (1959) and Carry On Regardless (1961). Rossington also played notable serious roles in Saint Joan (1957) and the classic 1960 British "New Wave" film Saturday Night and Sunday Morning, playing alongside Albert Finney in the latter's first starring role. In 1958 he acted in the first of two Titanic films, A Night to Remember, as a steward unable to communicate with non-English speaking passengers. Rossington would return in his second Titanic film playing the Sergeant-at-Arms in S.O.S. Titanic in 1979.

In 1962 Rossington played the uncredited role of Corporal Jenkins in Lawrence of Arabia, and later appeared in The Longest Day (1962), Those Magnificent Men in Their Flying Machines (1965), Tobruk playing Alfie (1967) and The Charge of the Light Brigade (1968). In 1972, he appeared in Young Winston and the cult horror film Death Line with Donald Pleasence.

From the 1970s onwards, Rossington mainly appeared on television, including roles in His and Hers, The Wednesday Play, Casanova, Carry On Christmas, Crown Court, I, Claudius, Z-Cars, Big Jim and the Figaro Club (1981, in the title role of "Big Jim"), The Bill and Last of the Summer Wine. His final appearances before his death were Heartbeat in 1996, Sharpe's Regiment as Sergeant Horatio Havercamp, also in 1996, and What's a Carry On? in 1998.

Rossington did some radio, returning to the part of Big Jim in the BBC Radio 4 version of Big Jim and the Figaro Club. He made six half-hour episodes in 1987.

Norman Rossington gave his hobbies as woodwork, skiing, golf and languages. He was married twice. His second marriage, on 19 January 1999 to Cindy Barnes, lasted until his death aged 70 a few months later. Rossington spent many of his last years living in a small terraced house in Hale, Cheshire. He would cycle around the village daily and was pleased to talk to those he met with tales from his career. He died in Manchester after a six-month battle with cancer. The village of Hale came out to pay their respects following his death.