Finney earned his third Best Actor in a Leading Role Oscar nomination playing an aging actor in the 1983 stage adaptation The Dresser, opposite Tom Courtenay. He made his final credited film appearance in Skyfall (2012).
"It was a privilege to work with him and an honor to have had him as part of our Bond family", said the pair in a statement issued via the official James Bond Twitter account. His screen breakthrough came later that year in Saturday Night and Sunday Morning, which rocketed him to stardom.
Born in 1936, Finney, a bookmaker's son, grew up in Manchester, northwest England and graduated from the Royal Academy of Dramatic Art in 1955.
Albert Finney has died.
But stardom came to Finney anyway in "Tom Jones" where he won over audiences worldwide with his good-natured, amusing and sensual portrayal of an 18th-century English rogue.
Displaying the versatility of a virtuoso, Finney portrayed Winston Churchill, Pope John Paul II, a southern American lawyer, an Irish gangster and an 18th-century rogue, among dozens of other roles over the years.
Legendary actor Albert Finney died yesterday, of an unknown cause.
"I was the first man to be seen sleeping with another man's wife in an English film", said Finney of his role as Arthur, a hard-living factor worker juggling affairs with two women while living at home. Nominated four times for the best actor Academy Award, and once for best supporting actor, Finney got his start at the Royal Shakespeare Company before landing memorable roles in Tom Jones, Murder on the Orient Express, Erin Brockovich, Big Fish, and-his last film-Skyfall.
Others paying tribute included Bernadette Peters, who starred alongside Finney in the 1982 film version of musical Annie; The Wire creator David Simon; Mission: Impossible filmmaker Christopher McQuarrie; The Late Show host Stephen Colbert; US actress Rosanna Arquette; and British actor, writer, and comedian David Walliams.
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.
News of Albert Finney dead was confirmed by a publicist to The Guardian. His marriage to Jane Denham lasted from 1957 to 1961 and Wednesday Anouk Aimeé in 1970.
Emmys: Outstanding lead actor for The Gathering Storm. Roberts won her first Oscar for the role. Funeral arrangements weren't immediately known.