His family said in a statement that the 81-year-old died of complications from his battle with cancer, the Dallas Morning News reported.
He passed away in a hospital in Dallas, his family added.
He had suffered from liver cancer and cirrhosis of the liver in the 1990s after decades of drinking.
Dallas, which made its premiere on the CBS network in 1978, made Hagman a superstar.
The show quickly became one of the network's top-rated programmes, built an international following and inspired a spin-off, imitators and a revival in 2012.
The popularity of Dallas made Hagman one of the best-paid actors in television and earned him a fortune. He lost some of it, however, in bad oil investments before turning to real estate.