His Dallas co-stars Linda Gray and Patrick Duffy, who played his wife Sue Ellen and brother Bobby, were at his bedside, The Sun newspaper reports.
Among those confirming the death were Linda Gray's agent, Jeffrey Lane, The Dallas Morning News said.
Hagman had a liver transplant in 1995 after years of alcoholism. He revealed how he used to down bottles of champagne on the Dallas set.
He married Maj Axelsson in 1954 and the couple had two children.