New Jersey-born Gandolfini went to Italy to attend a film festival in Sicily.
He won three Emmy awards for his role as Tony Soprano, a mafia boss juggling his criminal career and family life. "It is with immense sorrow that we report our client James Gandolfini passed away today while on holiday in Rome, Italy," said his managers in a statement.
"Our hearts are shattered and we will miss him deeply. He and his family were part of our family for many years and we are all grieving." HBO said the star of The Sopranos, which aired on the cable channel from 1999-2007, would be "deeply missed".
"He was 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," said its statement.
"He touched so many of us over the years with his humour, his warmth and his humility." Gandolfini was born in Westwood, New Jersey, to a school dinner lady and a bricklayer, both of Italian background.
He worked as a bartender and a club manager before his acting career took off on Broadway in 1992. His breakthrough role came a year later playing a mobster in the movie True Romance.