Burr Steers said Vidal died at his home in the Hollywood Hills at about 6.45pm local time on Tuesday of complications from pneumonia.
Mr Steers said Vidal had been living alone and had been sick for “quite a while”.
The acerbic Vidal was known for such best-selling novels as Burr and Myra Breckenridge, the play The Best Man, and for essays on everything from politics and literature to sex and religion.
In the 1960s and 70s he was a fixture on talk shows and other television programmes and feuded openly with Norman Mailer, William Buckley and others.
He also worked on screenplays and appeared in several films, including Bob Roberts and With Honors. His work in Hollywood also included writing the script for Suddenly Last Summer, based on Williams’s play and starring Elizabeth Taylor, and adding a subtle homoerotic context to Ben-Hur.
His works included hundreds of essays; best-selling novel Lincoln; the groundbreaking The City And The Pillar, among the first novels about openly gay characters; and political drama The Best Man, revived on Broadway in 2012.
Tall and distinguished looking, with a haughty baritone not unlike that of his conservative arch-enemy Buckley, Vidal appeared cold and cynical on the surface. But he bore a melancholy regard for lost worlds, for the primacy of the written word, for “the ancient American sense that whatever is wrong with human society can be put right by human action”.
A long-time critic of American militarism, Vidal was, ironically, born at the United States Military Academy in West Point, New York, his father’s alma mater.
He grew up in a political family. His grandfather, Thomas Pryor Gore, was a US senator from Oklahoma. His father, Gene Vidal, served briefly in President Franklin Roosevelt’s administration and was an early expert on aviation. Aviator Amelia Earhart was a family friend and reported lover of Gene Vidal.