Gandolfini, who won three Emmys and a Golden Globe for his depiction of troubled mob boss Tony Soprano on the popular cable TV series, was in Italy for the Taormina Film Fest in Sicily.
He was to have been given an award by the country's oldest festival, before participating in a roundtable discussion this weekend.
Edie Falco, the on-screen "Sopranos" wife of Gandolfini, paid tribute to her late co-star, saying their on-screen relationship was "one of the greatest" she had ever known.
"I am shocked and devastated by Jim's passing. He was a man of tremendous depth and sensitivity, with a kindness and generosity beyond words," she said in a statement.
"I consider myself very lucky to have spent 10 years as his close colleague. My heart goes out to his family, as those of us in his pretend one hold on to the memories of our intense and beautiful time together.
"The love between Tony and Carmela was one of the greatest I've ever known," she added.
The 51-year-old Gandolfini had stopped off in Rome en route to the festival and had spent Wednesday sightseeing with his teenage son Michael, before collapsing in the hotel bathroom, local media reports said.
ANSA news agency said Gandolfini had been seen chatting and smiling as he signed autographs in the morning, and had dined in the hotel in the evening with his son and sister.
It was Michael who had called for help when his father failed to respond, TMNews said.
"At around 22:00 Mr. James Gandolfini, on holiday in Rome and a guest in the hotel Exedra, fell ill while he was in his room. The family contacted staff" who called an ambulance, the hotel said.
HBO, the cable TV channel on which "The Sopranos" aired, issued a statement saying: "We're all in shock and feeling immeasurable sadness at the loss of a beloved member of our family."
The actor had a long film and stage career before lending his heavy stature and big grin to play a depressed mafioso in "The Sopranos," the celebrated series that ran from 1999 to 2007.
ANSA said Gandolfini's first wife, Marcy Wudarski -- Michael's mother -- was on her way to Rome.
The burly actor is also survived by his wife, Deborah Lin, whom he married in 2008 and their nine-month old daughter, according to the Los Angeles Times.
Organisers of the Taormina festival said they were "deeply saddened" to learn of the death of Gandolfini and were planning a special tribute to him.
"Sopranos" creator David Chase called Gandolfini a genius.
"Anyone who saw him even in the smallest of his performances knows that," he said. "He is one of the greatest actors of this or any time. A great deal of that genius resided in those sad eyes."
Gandolfini was born on September 18, 1961. His parents were Italian immigrants -- his father was a bricklayer, and later a high school custodian, while his mother worked in a cafeteria.
His parents insisted that he go to college, and after some initial resistance Gandolfini graduated with a degree in communications from Rutgers University in 1983.
The future Tony Soprano began acting in the New York theatre, making his Broadway debut in the 1992 revival of "A Streetcar Named Desire" with Jessica Lange and Alec Baldwin.
His breakthrough role came as a hitman in Tony Scott's 1993 "True Romance," which he followed with "She's So Lovely" (1997), "8MM" (1999), "The Mexican" (2001), "The Man Who Wasn't There" (2001) and "In the Loop" (2009).
Last year, Gandolfini played former CIA director Leon Panetta in the Oscar-winning Osama bin Laden manhunt movie "Zero Dark Thirty," while his last big-screen movie was "The Incredible Burt Wonderstone".