Mayhew died Tuesday at age 74 at his home in North Texas. He is survived by his wife, Angie, and three children.
Mayhew famously portrayed Chewbacca in five Star Wars films, including the original Star Wars in 1977, The Empire Strikes Back in 1980, Return of the Jedi in 1983, Revenge of the Sith in 2005 and The Force Awakens in 2015.
Chewbacca, a Wookiee from the planet Kashyyyk, was Han Solo's (Ford) partner and co-pilot aboard the Millennium Falcon.
"Peter Mayhew was a kind and gentle man, possessed of great dignity and noble character," Ford said in a statement. "These aspects of his own personality, plus his wit and grace, he brought to Chewbacca. We were partners in film and friends in life for over 30 years and I loved him. He invested his soul in the character and brought great pleasure to the Star Wars audience."
"Chewbacca was an important part of the success of the films we made together. He knew how important the fans of the franchise were to its continued success and he was devoted to them. I an millions of others will never forget Peter and what he gave us all. My thoughts are with his dear wife, Angie, and his children. Rest easy, my dear friend."
Hamill, who portrays Luke Skywalker in Star Wars, posted a photo with Mayhew on Twitter.
"He was the gentles of giants -- A big man with an even bigger heart who never failed to make me smile & a loyal friend who I loved dearly -- I'm grateful for the memories we shared & I'm a better man for just having known him. Thanks Pete #RIPPeterMayhew #Heartbroken," Hamill wrote.
Williams, who portrayed Lando Calrissian, posted, "Much more than Chewie to me...My heart hurts...I will miss you dear friend...thanks for the great memories! #RIPPeterMayhew."
Star Wars creator George Lucas said in a statement, "Peter was a wonderful man. He was the closest any human being could be to a Wookiee: big heart, gentle nature...and I learned to always let him win. He was a good friend and I'm saddened by his passing."
Filmmaker J.J. Abrams, who directed Mayhew in The Force Awakens, tweeted, "Peter was the loveliest man...kind and patient, supportive and encouraging. A sweetheart to work with and already deeply missed."
Actor Joonas Suotamo, who took over the role of Chewbacca, said on Twitter, "Peter's warm welcome when I came aboard as his double in The Force Awakens meant so much to me. Studying the character he helped create was always a daunting task, but one that was made easier by his tutelage and kindness as we sought to bring Chewbacca to life for a new generation. He was an absolutely one-of-kind gentleman and a legend of unrivaled class and I will miss him."
Filmmaker Rian Johnson, who directed The Last Jedi, said on Twitter, "RIP Peter Mayhew. To create a beloved character with warmth and humor is a testament to any actor's spirit. To do it under a half ton of yak hair takes a true legend."