He passed away at his home in Texas on 30 April with his family by his side, a statement said.
The British-American actor played giant Wookiee warrior Chewbacca in the original trilogy beginning in 1977 as well as later films until 2015.
"He put his heart and soul into the role of Chewbacca and it showed in every frame," his family said.
London-born Mayhew played Chewbacca in the original Star Wars trilogy, episode three of the prequels and the New Trilogy.
Star Wars creator George Lucas had wanted a tall actor to play Chewbacca - but initially considered 6ft 6in (1.98m) tall David Prowse for the role.
However Prowse instead wanted to play Darth Vader so Lucas then turned to Mayhew, who at 7ft 2in (2.18m) was chosen purely for his height. His face was never seen in the all the Star Wars films he played in.
"He fought his way back from being wheelchair-bound to stand tall and portray Chewbacca once more in Star Wars: The Force Awakens," his family said.
Mayhew also consulted on The Last Jedi, released in 2017, in an attempt to pass on the secrets of the role to his successor Finland's Joonas Suotamo.
Mayhew's family said "the Star Wars family meant so much more to him than a role in a film".
"The relationships that began then grew into the friends and family that he would love for decades to come."
The statement also said the actor had been "heavily involved" with non-profit organisations, and had launched his own foundation, which they said supported "everything from individuals and families in crisis situations to food and supplies for children of Venezuela".
Mayhew's family did not say what the cause of his death was.
A memorial service for friends and family would be held on 29 June, and a separate memorial for fans would take place in December, the statement said.
The London-born actor, who was 7ft 2in (2.18m) tall, is survived by his wife Angie and three children.
Mark Hamill, who played Luke Skywalker in the original Star Wars films, described Mayhew as "the gentlest of giants".
"A big man with an even bigger heart who never failed to make me smile and a loyal friend who I loved dearly," Hamill tweeted.