Hagman died at a Dallas hospital of complications from cancer, said the statement posted on Hagman's official web site early Saturday.
"Larry's family and close friends had joined him in Dallas for the Thanksgiving holiday. When he passed, he was surrounded by loved ones. It was a peaceful passing, just as he had wished for. The family requests privacy at this time."
Hagman shot to television superstardom in 1978 with the role of J.R. Ewing, the scheming Texas oil tycoon, in the prime-time soap opera "Dallas." He was the villain viewers loved to hate.
Co-stars, fellow actors grieve over loss of Larry Hagman
In 1980, the show became a mega-hit with the "Who Shot J.R.?" plot line that left Americans guessing who pulled the trigger.
The answer came on November 21, 1980, in an episode dubbed "Who Done It?." More than 350 million viewers tuned in around the world to find out Kristen Shepherd, the sister of J.R.'s wife, shot him. It remains one of the most watched television episodes in history.
Ewing survived that shooting, and Hagman and the rest of the cast thrived for 14 seasons total before bowing out in 1991.
He reprised the role for TNT's reboot of the series "Dallas" in June 2012. Hagman filmed appearances for the show's second season, which is set to air in January. (Like CNN, TNT is a division of Time Warner and Turner Broadcasting.)
It was a role in which he clearly reveled, even developing a trademark laugh for the character. At one point, Hagman made up fake $100 bills emblazoned with his face and the words "In Hagman We Trust" to hand out to fans.
In one of his final interviews on CNN, Hagman appeared alongside original "Dallas" cast members Linda Gray (Sue Ellen) and Patrick Duffy (Bobby) on "Piers Morgan Tonight."
During the interview, Morgan described the character of J.R. Ewing as "the dark dealer of evil scheming."
"Moi?" Hagman said, breaking into a wide smile.
In a statement released Friday by Gray's publicist to KNBC-TV in Los Angeles, the actress described Hagman as "my best friend for more than 35 years."
"He was the pied piper of life and brought joy to everyone he knew. He was creative, generous, funny, loving and talented and I will miss him enormously. He was an original and lived life to the full and the world was a brighter place because of him," the statement said.
Hagman told Morgan when he was first approached about doing the "Dallas" remake, the first question he asked was: "Are my friends going to be on the show?"
"I wouldn't be doing it without them," he said.
Word of Hagman's passing spread quickly late Friday and early Saturday, with celebrities and fans mourning his death.