"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.
Much-loved British actor Bob Hoskins has passed away at the age of 71"We ask that you respect our privacy during this time and thank you for your messages of love and support."
The sad news comes less than two years after the star of Who Framed Roger Rabbit announced his retirement from acting after being diagnosed with Parkinson's disease.
At the time, his agent said that after a "wonderful career" spanning four decades, the star was withdrawing from acting to spend time with his family.
"He wishes to thank all the great and brilliant people he has worked with over the years, and all of his fans who have supported him during a wonderful career," read the August 2012 statement.
Bob Hoskins starred in the 1998 film Who Framed Roger Rabbit
"Bob is now looking forward to his retirement with his family, and would greatly appreciate that his privacy be respected at this time."
Bob's breakthrough came in 1980, when he played Harold Shand in the British gangster film The Long Good Friday, alongside Helen Mirren.
His portrayal of George in Neil Jordan's film Mona Lisa, about a high-class call girl, won him numerous awards including a Golden Globe for best actor, a Bafta and an Academy Award nomination.
Bob Hoskins won numerous awards for his portrayal of George in the 1986 film, Mona Lisa
He was again nominated for best supporting actor at the Globes for his role in Mrs Henderson Presents, a 2005 British comedy, starring Dame Judi Dench.
Other notable appearances included Smee in Steven Spielberg's 1991 Peter Pan film, Hook. He played the same character in Neverland in 2011 which also starred Anna Friel, Rhys Ifans and the voice of Keira Knightley as Tinker Bell.
Bob's last film appearance was in the 2012 film Snow White And The Huntsman, in which he played one of the dwarves opposite Kristen Stewart.
Bob Hoskins with his second wife, Linda Banwell