Disney announced on Tuesday (October 30) that it is buying Lucasfilm for $4.05 billion (£2.5bn) and will release Star Wars: Episode 7 in 2015, with two more sequels to come.
Mayhew - who played Chewbacca - has now suggested that Disney is the perfect home for the Star Wars franchise.
"I have no doubt Disney will respect and continue the legacy of Lucasfilm," Mayhew told TMZ. "I have worked with Disney for many years during their Star Wars Weekends Celebration and seen how much they love the films and the fans."
Mayhew went on to say that he was impressed with Disney's vision for Marvel's The Avengers, adding: "[Disney] has an excellent track record for listening to the creator's voice!"
The Lucasfilm-Disney deal has also received the backing of Ahmed Best - who played Jar Jar Binks - and young Boba Fett actor Daniel Logan.
Disney CEO Bob Iger has hinted to reporters that a new Star Wars television series could be produced to air on Disney XD in the near future.
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Photo gallery - Star Wars rare behind-the-scenes pictures: