Hoskins’ agent said he died on Tuesday in hospital, surrounded by family.
The star won a Bafta and was Oscar nominated in 1987 for crime drama Mona Lisa, in which he starred opposite Sir Michael Caine and Robbie Coltrane.
“We are devastated by the loss of our beloved Bob,” the actor’s wife Linda and children Alex, Sarah, Rosa and Jack said in a statement.
“Bob died peacefully at hospital last night surrounded by family, following a bout of pneumonia.
“We ask that you respect our privacy during this time and thank you for your messages of love and support.”
Actor Sir Michael Caine, who starred with him in the films Mona Lisa and Last Orders, said: “He was one of the nicest and best actors I have ever worked with”.
Hoskins, who was born in Suffolk but grew up in London, started out on the stage before embarking on a television and film career.
On the small screen, he appeared in shows such as Play for Today, On the Move, Van der Valk and BBC drama The Street.
On film, his credits also included Mermaids, Hook, Mrs Henderson Presents and Made in Dagenham.
His last film role was as one of the dwarves in 2012’s Snow White and the Huntsman, starring Kristen Stewart.
Dame Judi Dench, who starred opposite Hoskins in Mrs Henderson Presents, told the BBC News website: “I’m so very sorry to hear this news, and am thinking of his family at this sad time.”
Hoskins was Bafta nominated twice prior to his Mona Lisa win, for The Honorary Consul in 1984 and The Long Good Friday in 1982.
He was also nominated for a television Bafta for his role in Dennis Potter’s BBC musical drama, Pennies from Heaven.
UK film critic Jason Solomons called The Long Good Friday “a great Londoner’s movie”.
“London ran through him like a stick of rock,” he added.
Tributes to the actor have appeared swiftly on Twitter, with Bafta saying it was “deeply saddened” to learn of his death.
Actress Vicky McClure, who worked with Hoskins on Shane Meadows’ 1999 film A Room for Romeo Brass: “He was one of the best. I feel honoured to have met & worked with him.”
Stephen Fry added: “That’s awful news. The Long Good Friday [is] one of the best British movies of the modern era. A marvellous man.”
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Tempus fugit