Finney was born in Pendleton, Salford, Lancashire, to Alice Hobson and Albert Finney, Sr., a bookmaker. He was educated at Tootal Drive Primary School, Salford Grammar School and the Royal Academy of Dramatic Art.

He has a son by his first wife, Jane Wenham: Simon, who works in the film business as a camera operator.

From 1970 to 1978 he was married to French actress Anouk Aimée.

Finney is close friends with his one time classmate Peter O'Toole. He is also good friends with Gene Wilder, whom he met through chance, and accepted a quick cameo in Wilder's The Adventure of Sherlock Holmes' Smarter Brother.[citation needed]

Finney is a graduate of the Royal Academy of Dramatic Art and a member of the Royal Shakespeare Company. His career began in the theatre; he made his first appearance on the London stage in 1958 in Jane Arden's The Party, directed by Charles Laughton, who starred in the production along with his wife, Elsa Lanchester.

His first film appearance was a role in Tony Richardson's The Entertainer (1960), which starred Laurence Olivier, but he made his breakthrough with his portrayal of a disillusioned factory worker in Karel Reisz's film version of Alan Sillitoe's Saturday Night and Sunday Morning. This led to a series of "Angry Young Man" roles in kitchen sink dramas, before he starred in the Academy Award-winning 1963 film Tom Jones. Prior to this, Finney had been chosen to play T. E. Lawrence in David Lean's production of Lawrence of Arabia, but the actor quit after four days of shooting.

After Charlie Bubbles (1968), which he also directed, his film appearances became less frequent as he focused more on acting on stage. During this period, one of his high-profile film roles was as Agatha Christie's Belgian master detective Hercule Poirot in the 1974 film Murder On The Orient Express. Finney became so well-known for the role that he complained that it typecasted him for a number of years. "People really do think I am 300 pounds with a French accent" he said.

Despite being known for his dramatic roles, Finney appeared and sang in two musicals: Scrooge and the Hollywood film version of Annie, which was directed by John Huston, who would direct him once again in The Volcano two years later. He also sings in Tim Burton's Corpse Bride.

Finney made several television productions for the BBC in the 1990s, including The Green Man (1990), based on a story by Kingsley Amis, the acclaimed drama A Rather English Marriage (1998) (with Tom Courtenay), and the lead role in Dennis Potter's final two plays, Karaoke and Cold Lazarus in 1996 and 1997. In the latter he played a frozen, disembodied head.

Finney also made an appearance at Roger Waters' The Wall Concert in Berlin, where he played "The Judge" during the performance of "The Trial".