The star, who landed a best actor Oscar nomination for Mona Lisa, retired from screen work in 2012 after he was diagnosed with Parkinson's disease.
His family released a statement saying he died last night in hospital.
His wife Linda and children Alex, Sarah, Rosa and Jack said: "We are devastated by the loss of our beloved Bob.
"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."
The star, who was born Suffolk after his mother was evacuated from the capital, grew up in north London and left school aged 15 to work in a series of odd jobs while dreaming of getting into acting.
He claimed he got his big break by accident after being mistakenly called for a theatre audition, but he proved a natural and stage success lead him into TV and small film parts.
His breakthrough role came in Dennis Potter's 1978 series Pennies From Heaven in which he played the lovelorn sheet music salesman Arthur Parker.
His portrayal of doomed London gangster Harold Shand in The Long Good Friday made him a film star and he followed it with stand-out roles in Mona Lisa and The Cotton Club.
His role as George, the petty criminal who becomes entangled with a high-class hooker, in the 1986 hit Mona Lisa won him an Oscar nomination for leading actor and by the mid-1980s he was an established Hollywood star with appearances in blockbusters including Who Framed Roger Rabbit and opposite Cher in Mermaids.
The diminutive actor with the gravelly cockney accent - who often played rough-edged characters with a heart of gold - was also familiar to millions for his ad campaign for British Telecom in which he told viewers: "It's good to talk".
One role he is said to have regretted was playing one of the Super Mario Bros in the film of the same name based on the hit computer game.
He had a better time with a role he did not win - when a proposed move to replace Robert De Niro as Al Capone in The Untouchables fell through he was given a £20,000 pay-off by director Brian De Palma, prompting Hoskins to ask if he had any more films he did not want him to be in.
He continued to work steadily - appearing alongside Dame Judi Dench in wartime drama Mrs Henderson Presents, playing one of the seven dwarfs in Snow White And The Huntsman, starring Kristen Stewart, and appearing in British films including Made In Dagenham and Outside Bet.
The star - who had been married to his second wife, Linda, for more than 30 years - also moved into directing with The Raggedy Rawney and Rainbow.
Despite his flourishing big-screen career, Hoskins took a role in Jimmy McGovern's BBC1 series The Street in 2009, winning an international Emmy.
He announced his 2012 retirement after what he called a "wonderful career" and said he was looking forward to spending time with his family.
Culture Minister Ed Vaizey paid tribute, saying: "For decades, Bob Hoskins has entertained television and film audiences of all age groups around the world. The British film industry has lost one of its true greats, and my thoughts and sympathies go out to his family and friends."