The actor suffered a possible heart attack while traveling in Rome, a rep for HBO says. Gandolfini had been scheduled to take part in the Taormina Film Fest in Sicily.
"We're all in shock and feeling immeasurable sadness at the loss of a beloved member of our family," HBO says in a statement. "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."
"He touched so many of us over the years with his humor, his warmth and his humility," the statement continues. "Our hearts go out to his wife and children during this terrible time. He will be deeply missed by all of us."
Born in Westwood, N.J., Gandolfini graduated from Park Ridge High School, where he played basketball and participated in school plays, and went on to study communications at Rutgers University.
He kicked off his acting career in 1987 in Shock! Shock! Shock! and then appeared in the Melanie Griffith-starring A Stranger Among Us – as well as notably starring in 1993's True Romance as Virgil, a mob-enforcer.
After several mob-related roles over the years, Gandolfini got his big break in 1999 starring in The Sopranos.
Anthony Neste / / Time Life Pictures / Getty
Tony was a complicated, conflicted character, kind one moment, a violent sociopath the next, while also struggling with depression.
"He was a genius," said Sopranos creator David Chase. "Anyone who saw him even in the smallest of his performances knows that. He is one of the greatest actors of this or any time. A great deal of that genius resided in those sad eyes."
Chase added: "He wasn't easy sometimes. But he was my partner, he was my brother in ways I can't explain and never will be able to explain."
Gandolfini had a wide-ranging film career, appearing in Zero Dark Thirty, Get Shorty and The Mexican.
His most recent movie was The Incredible Burt Wonderstone, which also starred Steve Carell, Olivia Wilde and Jim Carrey.
"James Gandolfini was a kind, funny, wonderful guy," Wilde Tweeted. "I'm so lucky to have worked with him. Sending love to his family. Such a sad, sad day."
Gandolfini is survived by his wife Deborah Lin, their 8-month-old daughter Liliana, and son Michael, 13, from a previous marriage.