The cable channel, and managers Mark Armstrong and Nancy Sanders, say the 51-year-old Gandolfini died Wednesday while on holiday in Rome.
In a statement, HBO called the actor a great talent and a gentle and loving person.
Gandolfini played conflicted mob boss Tony Soprano in the groundbreaking HBO series that aired from 1999 to 2007.
His film credits included "Zero Dark Thirty" and "Killing Them Softly," and he appeared in the Broadway production "God of Carnage."
Statement from (Gandolfini's personal managers) Mark Armstrong and Nancy Sanders:
It is with immense sorrow that we report our client James Gandolfini passed away today while on holiday in Rome, Italy. 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.
We're all in shock and feeling immeasurable sadness at the loss of a beloved member of our family. 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. Our hearts go out to his wife and children during this terrible time. He will be deeply missed by all of us.
The Associated Press contributed to this report.