Gandolfini died while on holiday in Rome, the cable channel and Gandolfini's managers Mark Armstrong and Nancy Sanders said in a joint statement. No cause of death was given.
"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."
Gandolfini, who won three Emmy Awards for his role as Tony Soprano, worked steadily in film and on stage after the series ended. He earned a 2009 Tony Award nomination for his role in the celebrated production of "God of Carnage."
"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," said managers Armstrong and Sanders.
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." The channel expressed sympathy for his wife and children.
Joe Gannascoli, who played Vito Spatafore on the HBO drama, said he was shocked and heartbroken.
"Fifty-one and leaves a kid -- he was newly married. His son is fatherless now ... It's way too young," Gannascoli said.
Gandolfini's performance in "The Sopranos" was indelible and career-making, but he refused to be stereotyped as the bulky mobster who was a therapy patient, family man and apparently effortless killer.
In a December 2012 interview with The Associated Press, a rare sit-down for the star who avoided the spotlight, he was upbeat about a slew of smaller roles following the breathtaking blackout ending in 2007 of "The Sopranos."
"I'm much more comfortable doing smaller things," Gandolfini said in the interview. "I like them. I like the way they're shot; they're shot quickly. It's all about the scripts -- that's what it is -- and I'm getting some interesting little scripts."
He played Secretary of Defense Leon Panetta in Kathryn Bigelow's Osama bin Laden hunt docudrama "Zero Dark Thirty." He worked with Chase for the `60s period drama "Not Fade Away," in which he played the old-school father of a wannabe rocker. And in Andrew Dominick's crime flick "Killing Them Softly," he played an aged, washed-up hit man.
There were comedies such as the political satire "In the Loop," and the heartwarming drama "Welcome to the Rileys," which co-starred Kristen Stewart. He voiced the Wild Thing Carol in "Where the Wild Things Are."
Gandolfini grew up in Park Ridge, N.J., the son of a building maintenance chief at a Catholic school and a high school lunch lady.
While Tony Soprano was a larger-than-life figure, Gandolfini was exceptionally modest and obsessive -- he described himself as "a 260-pound Woody Allen."
In past interviews, his cast mates had far more glowing descriptions to offer.
"I had the greatest sparring partner in the world, I had Muhammad Ali," said Lorraine Bracco, who, as Tony's psychiatrist Dr. Melfi, went one-on-one with Gandolfini in their penetrating therapy scenes. "He cares what he does, and does it extremely well."
After earning a degree in communications from Rutgers University, Gandolfini moved to New York, where he worked as a bartender, bouncer and nightclub manager. When he was 25, he joined a friend of a friend in an acting class, which he continued for several years.
Gandolfini's first big break was a Broadway production of "A Streetcar Named Desire" where he played Steve, one of Stanley Kowalski's poker buddies. His film debut was in Sidney Lumet's "A Stranger Among Us" (1992).
Director Tony Scott, who killed himself in August 2012, had praised Gandolfini's talent for fusing violence with charisma -- which he would perfect in Tony Soprano.
Gandolfini played a tough guy in Tony Scott's 1993 film, "True Romance," who beat Patricia Arquette's character to a pulp while offering such jarring, flirtatious banter as, "You gotta lot of heart kid."
Scott called Gandolfini "a unique combination of charming and dangerous."
Gandolfini continued with supporting roles in "Crimson Tide" (1995), "Get Shorty" (1995), "The Juror" (1996), Lumet's "Night Falls on Manhattan" (1997), "She's So Lovely" (1997), "Fallen" (1998) and "A Civil Action" (1998). But it was "True Romance" that piqued the interest of Chase.
He shared a Broadway stage with Jeff Daniels, Hope Davis and Marcia Gay Harden in "God of Carnage" when he received the best-actor Tony nod. He was in "On the Waterfront" with David Morse and was an understudy in a revival of "A Streetcar Named Desire" in 1992 starring Alec Baldwin and Jessica Lange.
In his 2012 AP interview, Gandolfini said he gravitated to acting as a release, a way to get rid of anger. "I don't know what exactly I was angry about," he said.
"I try to avoid certain things and certain kinds of violence at this point," he said last year. "I'm getting older, too. I don't want to be beating people up as much. I don't want to be beating women up and those kinds of things that much anymore."
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