The Sopranos star was on vacation in Rome and was due to attend the 59th Taormina Film Festival in Sicily. He is survived by his wife Deborah Lin and two children, Michael, 13, and nine-month-old daughter Liliana Ruth.
In a statement Gandolfini's managers Mark Armstrong and Nancy Sanders confirmed the death, which happened on Wednesday.
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Cable channel HBO called the actor a 'special man, a great talent, but more importantly a gentle and loving person who treated everyone, no matter their title or position, with equal respect.'
We're all in shock and feeling immeasurable sadness at the loss of a beloved member of our family,' HBO said.
'He touched so many of us over the years with his humor, his warmth and his humility. Our hearts go out to his wife and children during this terrible time. He will be deeply missed by all of us.'
Gandolfini's wife, former model Deborah Lin, gave birth to a baby girl last October, and the couple married in Hawaii in 2008.
May his soul rest in peace.