Mayhew, who measured 7ft 2in (2.18m) in height, played the Wookie pilot and Han Solo's longtime friend in the original Star Wars trilogy from 1977, before reprising the role in Star Wars: The Force Awakens (2015), despite struggles with mobility and poor health.
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"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 in a statement.
Mark Hamill, who played Luke Skywalker alongside Mayhew, paid tribute to "the gentlest of giants".
"He was the gentlest of giants- a big man with an even bigger heart who never failed to make me smile & a loyal friend who I loved dearly," Hamill wrote on Twitter.
"I'm grateful for the memories we shared & I'm a better man for just having known him. Thanks Pete
#RIPPeterMayhew #Heartbroken @TheWookieeRoars"
John Boyega, who plays Finn in the current Star Wars trilogy, wrote on Instagram: "The happiness you brought to my life through Chewbacca was always enough but to meet you and experience your amazing heart was even better."
Billy Dee Williams, who played Lando Calrissian in the Star Wars film franchise, also paid tribute on Twitter.
Mayhew consulted on on The Last Jedi (2017) in order to assist his successor, Finnish actor Joonas Suotamo.
Suotamo said in a statement released on Twitter that he was "devastated to hear about the passing of my dear friend and mentor, the great Peter Mayhew".
"The Star Wars family meant so much more to him than a role in a film," Mayhew's family said.
"The relationships that began then grew into the friends and family that he would love for decades to come."