Baker made his name as the robot in the first Star Wars film in 1977 alongside Anthony Daniels's C-3PO character.
Star Wars creator George Lucas paid tribute to a "real gentleman" and Mark Hamill - Luke Skywalker in the films - said he had lost "a lifelong friend".
Born in Birmingham, Baker's other films include Time Bandits and Flash Gordon.
After starring in the original Star Wars film he went on to appear in the sequels, The Empire Strikes Back and Return of the Jedi, and the three prequels between 1999 and 2005.
Baker was a consultant on the last Star Wars production - The Force Awakens - but British actor Jimmy Vee was already lined up to take on the role of R2-D2 in the next film, due for release in 2017.