Managers for the actor, who played Tony Soprano in the hit mob series, confirmed the sad news on Thursday morning (20 June), saying James died while on holiday in Rome, Italy with his family.
"Our hearts are shattered and we will miss him deeply," said a statement.
It is believed that James, who had been due to attend the closing day of the Taormina Film Festival in Sicily this weekend, suffered a possible heart attack.
A statement from HBO, which produced The Sopranos, said: "We're all in shock and feeling immeasurable sadness at the loss of a beloved member of our family.
"He was 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."
The network added: "He touched so many of us over the years with his humour, 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."
New Jersey-born James won three Emmy Awards for his role as Tony in The Sopranos, and enjoyed success in film and on Broadway as well, with recent credits including the Oscar-winning Zero Dark Thirty.
James is survived by wife Deborah Lin and their nine-month-old daughter Liliana, and his teenage son Michael from his first marriage.