His impressive career saw him nominated for a number of awards, including an Oscar for Best Actor, though he didn't win.
His final role came in 2012 with Skyfall, in which he played Kincade. In the latter, he starred as an angry young factory worker who rebels against domestic ties.
Finney then became the face of British cinema's global explosion after being cast in the title role of Tom Jones, directed by The Entertainer's Tony Richardson.
Comedian and novelist David Walliams remembered him simply as "the lovely Albert Finney".
Finney with Susannah York in the 1963 classic film Tom Jones.
His Golden Globes were awarded for "Tom Jones", "Scrooge" and "The Gathering Storm", which also earned him an Emmy Award.
Finney was nominated four times for a best actor Oscar and once in the best supporting actor category.
Daniel Craig said "the world has lost a giant" as he paid tribute to Albert Finney, who has died aged 82 following a short illness.
Finney twice turned down official honours - a CBE in 1980 and a knighthood in 2000 - and revealed in 2011 he had overcome cancer after successful treatment.
Actor Rufus Sewell said he was "very sad" to hear about Finney's death, adding that he "had the enormous privilege of working with him early on".
Even during this extraordinary run of great roles, and his critically acclaimed television portrayal of the pope, Finney's life was not chronicled in People Weekly or other magazines, although the British press was fascinated with his marriage to the sultry French film star Anouk Aimee.
He played alcoholic ex-diplomat Geoffrey Firmin in Under the Volcano, which brought him his fourth Oscar nomination, and would go on to earn another nod in 2001 for Erin Brockovich.
Finney also found success on Broadway.
However, he's never been one to take such awards too seriously, and would rarely attend the ceremonies.
Finney married Penelope Delmage in 2006 and is survived by her and a son, Simon Finney.
Funeral arrangements for Finney have not been released yet.