"Larry was back in his beloved Dallas, re-enacting the iconic role he loved most," his family said in a statement via The Dallas Morning News. "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's rep says the late actor will be cremated.
His Dallas co-stars Linda Gray (who played his wife Sue Ellen) and Patrick Duffy (who played his brother Bobby) were reportedly at his bedside when he died, The Sun is reporting.
"Larry Hagman was my best friend for 35 years. He was the Pied Piper of life and brought joy to everyone he knew," Gray told ET in a statement. "He was creative, generous, funny, loving and talented, and I will miss him enormously. He was an original and lived life to the fullest ... The world was a brighter place because of Larry Hagman."
"Friday I lost one of the greatest friends ever to grace my life. The loneliness is only what is difficult, as Larry's peace and comfort is always what is important to me, now as when he was here," Duffy said in a statement. "He was a fighter in the gentlest way, against his obstacles and for his friends. I wear his friendship with honor."
Victoria Principal, who played Pamela Barnes Ewing, added, "Larry was bigger than life ... on screen and off. He is unforgettable, and irreplaceable, to millions of fans around the world, and in the hearts of each of us, who was lucky enough to know and love him. Look out God ... Larry's leading the parade."
Hagman, who also starred as Air Force Captain Anthony Nelson in I Dream of Jeannie, was last seen on television in TNT's Dallas reboot, where he returned to play his most well-known character.
"Larry Hagman was a giant, a larger-than-life personality whose iconic performance as J.R. Ewing will endure as one of the most indelible in entertainment history," Warner Bros., Dallas executive producers Cynthia Cidre and Michael M. Robin, and the show's cast and crew said in a statement. "He truly loved portraying this globally recognized character, and he leaves a legacy of entertainment, generosity and grace. Everyone at Warner Bros. and in the Dallas family is deeply saddened by Larry's passing, and our thoughts are with his family and dear friends during this difficult time."
"It was truly an honor to share the screen with Mr. Larry Hagman," Dallas reboot star Jesse Metcalfe, who plays Christopher Ewing, said in a statement. "With piercing wit and undeniable charm he brought to life one of the most legendary television characters of all time. But to know the man, however briefly, was to know a passion and dedication for life and acting that was profoundly inspirational."