The New York Times confirmed his Sunday death in West Sussex, England, but did not list a cause.
"It is true to say that nearly 100 percent of fencing in Britain today is directly or indirectly attributable to the work of this man," the academy said in a statement Monday.
Anderson coached numerous stars in some of their most famous swashbuckling roles. Among those with whom he worked were Errol Flynn, Sean Connery, Cary Elwes, Mandy Patinkin, Antonio Banderas, Ryan O'Neal, Charlie Sheen, Kiefer Sutherland, Oliver Platt and Chris O'Donnell. He also did masked villain Darth Vader's fight scenes on-screen in the original "Star Wars" trilogy, the Times said.
He is survived by his wife, Pearl, three children and several grandchildren.