He was 71.
A statement issued on behalf of his wife Linda and his children 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."
Hoskins announced his retirement from acting in 2012, saying at the time that he was suffering from Parkinson's disease, an incurable muscular disorder.
Hoskins started his career in the 1970s on British television shows such as "Thick as Thieves" and "Rock Follies of '77".
Moving into big film roles, his turn as a mobster in 1980s "The Long Good Friday" shot him to stardom and defined his tough guy persona.
He was nominated for a best actor Oscar in 1987 for "Mona Lisa", in which he starred opposite Sir Michael Caine and Robbie Coltrane, and won a Golden Globe award.
"He was one of the nicest and best actors I have ever worked with," Caine said, quoted by the BBC.
The Suffolk-born actor became a staple face in the British film industry, often playing Cockney-speaking characters in both comedy and drama genres with his trademark gravelly voice.
His big Hollywood break came in 1988 when he played Eddie Valiant in "Who Framed Roger Rabbit," a role for which he received a Golden Globe nomination. He then went on to play roles in 1990's "Mermaids" and 1991's "Hook."
He portrayed Hoover in the 1995 movie "Nixon", earning a Screen Actors Guild nomination.
In his later years he took on parts in smaller films, including a role in "Made in Dagenham" about women seeking equal pay with male workers at a car plant near London.
He also played the voice of the character Winston in the 2006 film "Garfield: A Tail of Two Kitties".
Film critic Nick James, who edits the British Film Institute's "Sight & Sound" magazine, said Hoskins was one of the most recognisable British actors in British and American films of the 1970s and 1980s.
"He's that kind of character - very, very versatile, a huge range of emotions," James said on Sky television.
"His career really spans a great period in British work and he's all over it."