The fighting trainer was best known for his work on Star Wars and Lord of the Rings - the latter of which involved the crafting of various fighting styles for the different races.
Anderson played Darth Vader during the lightsaber duels in the original Star Wars trilogy.
The former British competitive fencer passed away peacefully in hospital at 4am on January 1, reports The British Academy of Fencing.
Mark Hamill highlighted Anderson's contribution to Star Wars for the first time in a 1983 interview.
"Bob Anderson was the man who actually did Vader's fighting," he said.
"It was always supposed to be a secret, but I finally told [George Lucas] I didn't think it was fair anymore.
"Bob worked so bloody hard that he deserves some recognition. It's ridiculous to preserve the myth that it's all done by one man."
Anderson also worked on The Princess Bride, First Knight, Highlander, Zorro, the first Pirates of the Caribbean movie and several James Bond films.