Mr Hagman played the scheming J.R. Ewing throughout the show’s original 13 year run and, to the delight of fans around the world, returned to the part when the series was revived earlier this year.
Prior to his work on Dallas Hagman starred as astronaut Tony Nelson in the 1960s television comedy I Dream of Jeannie.
His film work included roles in political drams Nixon and Primary Colors.
In a statement announcing his passing, Mr Hagman’s family said: “Larry was back in his beloved Dallas, re-enacting the iconic role he loved most..he was surrounded by loved ones.”
Co-star Linda Gray, who plays Sue Ellen, said: “”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.”
The show’s producers paid tribute to “a wonderful human being and an extremely gifted actor.”
“We will be forever thankful that a whole new generation of people got to know and appreciate Larry through his performance as J.R. Ewing. Our thoughts and prayers are with his family at this very difficult time.”
Richard Desmond, owner of Channel 5 which airs Dallas in the UK, said he was “very sad to hear the news that Larry Hagman has died.”
Mr Desmond added: “ He was the ultimate professional and a very good guy who I had the privilege of meeting a number of times, most recently when he, Linda and Patrick came to London to help launch Dallas on Channel 5. He was very funny and made us all laugh. This is a very sad day for his family and friends.”
Channel 5 is to air a 30-minute programme: A Tribute to Larry Hagman: At home with JR, tomorrow night at 9pm.