KABC-TV in Los Angeles reports that Durst died of natural causes due to a "litany of medical issues from which he was suffering."
In September, Durst was convicted in Los Angeles of fatally shooting Berman in 2000. He was later sentenced to life in prison. Weeks later, he was charged with murder in connection with the 1982 disappearance of his wife, Kathie, in New York state.
Prosecutors claimed that Durst murdered Berman to cover up his involvement in his wife's death.
Durst became well known through the 2015 HBO docuseries "The Jinx," which told the story of his life and the mysterious disappearances of several people close to him.
In the final episode of the series, Durst appeared to admit to several murders.
"What the hell did I do? Killed them all, of course,” Durst muttered to himself while staring at himself in a bathroom mirror.
Durst was arrested in New Orleans hours before the final episode of The Jinx aired.
Durst's murder conviction will be vacated because he died while the appeals process was taking place, a Los Angeles prosecutor told PEOPLE.
Laurie Levenson, a law professor at Loyola Law School, told The Associated Press that California law requires a conviction to be vacated if the defendant dies while the case is being appealed.