The gruff Londoner, who rose to fame in British gangster films in the 1980s and went on to have a long career as a Hollywood character actor, died in hospital on Tuesday night, they said in a statement.
Hoskins, who was nominated for an Oscar and won a Golden Globe for his role in "Mona Lisa" in 1986, retired from acting in 2012 after being diagnosed with Parkinson's disease.
“We are devastated by the loss of our beloved Bob, " said a statement from his wife Linda and the couple's two children Rosa and Jack, and Hoskins's two children from his first marriage, Alex and Sarah.
"Bob died peacefully at hospital last night surrounded by family, following a bout of pneumonia," said the statement issued by acting agent Clair Dobbs.
"We ask that you respect our privacy during this time and thank you for your messages of love and support."
Hoskins left school at the age of 15 and claimed he only got his break in acting by accident, after being mistakenly called for a theatre audition.
He began as a television actor and broke through into film with his portrayal of a doomed London gangster in "The Long Good Friday" in 1980, which won him a Bafta nomination.
One of his best known roles was as the detective trying to work out "Who Framed Roger Rabbit", the eponymous cartoon hero, for which he was nominated for a Golden Globe in 1989.
More recent success came with a Globe nomination for "Mrs Henderson Presents" with Judi Dench, while his last role was one of the seven dwarves in the film "Snow White and the Huntsman", starring "Twilight" actress Kristen Stewart.