The actor was best known for his roles in Erin Brockovich, Murder On The Orient Express and Annie.
A statement from his family said: “Albert Finney, aged 82, passed away peacefully after a short illness with those closest to him by his side.
“The family request privacy at this sad time.”
The five-time Oscar nominee, who was born in Salford in 1936, made his movie debut with a small part in The Entertainer in 1960.
Director Tony Richardson then offered Finney the lead in kitchen-sink drama Saturday Night and Sunday Morning, and period romp Tom Jones, which made him a major star.
He most recently starred in the James Bond film Skyfall and the Bourne films.