The actor, who was famed for playing J.R. Ewing on the hit show, died at a Dallas hospital on Friday after complications with his recent battle with throat cancer.
He returned to Dallas to reprise his role as cunning villain J.R. in the show's reboot, which started airing in June of this year.
'Larry was back in his beloved Dallas, re-enacting the iconic role he loved most,' the star's family said in a statement.
'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.'
His co-star Linda Gray, who played his on-screen wife Sue Ellen Ewing, was at his bedside when he died at 4.20pm, her agent Jeffrey Lane has stated.
Mr. Lane added that Patrick Duffy, who played his brother Bobby, was also at Hagman's bedside at Medical City Dallas Hospital.
'They had been friends for 35 years and they had worked together for many years, so obviously it is devastating,' Mr. Lane told The Sun.
Hagman announced in October 2011 that he had a 'treatable' form of throat cancer and would receive treatment while filming the Dallas reboot.
At the time the star said: 'As J.R. I could get away with anything - bribery, blackmail and adultery. But I got caught by cancer. I do want everyone to know that it is a very common and treatable form of cancer.
'I will be receiving treatment while working on the new Dallas series. I could not think of a better place to be than working on a show I love, with people I love.'
The late actor added: 'Besides, as we all know, you can't keep J.R. down!'
He is survived by wife Maj, who he married in in 1952.