A spokesperson for Finney's family confirmed the news to UK outlet The Sun.
They issued a short statement.
"He passed away peacefully after a short illness with those closest to him by his side. The family request privacy at this sad time."
In 2011 Finney revealed he was suffering from kidney cancer, however The Sun reports that he passed away due to complications from a chest infection.
Finney starred in more than 60 films spanning his extensive career.
He was born on May 9, 1936 in Pendelton, Greater Manchester and studied drama before being cast in William Shakespeare plays. He had his first major lead role in Saturday Night and Sunday Morning which made him known in the industry. From there, he was cast in numerous big name roles in major films.
Throughout his career, Finney showed his versatility as an actor, being cast as everything from Scrooge to Hercule Poirot in Agatha Christie's Murder On The Orient Express, before portraying the role of Daddy Warbucks in the 1982 musical Annie.
The star was married three times and lived with wife Pene Delmage in London until his last days.
Fellow actors have paid tribute to the legend on social media.
David Morrissey took to Twitter, writing: "One of the true great. Both on stage and screen. A powerhouse of an actor. A real hero of mine. RIP Albert Finney".
Tweeted Rufus Sewell: "Very sad to hear about Albert Finney. I had the enormous privilege of working with him early on. Apart from being effortlessly great he was also a great all round example of how to behave".
He will be sorely missed.