He died in hospital on Thursday from health complications after living with Parkinson's disease for many years, his agent said.
"He had a long and happy career spanning more than 45 years," a statement said.
"He was devoted to his wife, three sons, and 10 grandchildren and they will miss him terribly."
Bulloch was best known for playing bounty hunter Boba Fett in The Empire Strikes Back and Return of the Jedi.
The character has since featured in the second season of Star Wars spin-off series, The Mandalorian.
Bulloch also appeared in James Bond film Octopussy in 1983, and the BBC TV series Doctor Who in the 1970s.
Daniel Logan, who took over from Bulloch to play the role of Boba Fett in the 2002 film Star Wars: Episode II - Attack of the Clones, paid tribute to the actor on Instagram.
"RIP Legend I'll never forget all you've taught me. I'll love you forever," he wrote.
"Conventions won't be the same without you. May the force be with you always."
Mark Hamill, who played Luke Skywalker in the original Star Wars trilogy, described Bulloch as the "quintessential English gentleman".
"A fine actor, delightful company and so kind to everyone lucky enough to meet or work with him," he wrote on Twitter.
"I will deeply miss him and am so grateful to have known him."
And Billy Dee Williams, best known as Lando Calrissian in the Star Wars franchise, wrote on Twitter: "Today we lost the best bounty hunter in the galaxy."
A post from the official Star Wars Twitter account said Bulloch's "unforgettable performance" as Boba Fett "captivated audiences since he first appeared".
"He will be remembered not only for his iconic portrayal of the legendary character, but also for his warmth and generous spirit which have become an enduring part of his rich legacy," the post said.
Born in Market Harborough, Leicestershire, Bulloch's first major role was in the musical film Summer Holiday in 1963, aged 17, when he starred alongside pop star Sir Cliff Richard.