Jack's agent Jill McCullough confirmed his death, reports bbc.com.
He died in a Surrey hospital on Tuesday. McCullough said she has been flooded with tributes to one of the acting world's "brightest and clearest voices".
She said Jack couldn't see his wife in his final days because she was quarantined in Australia.
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The British actor, who was seen in "Star Wars: The Force Awakens" (2015) and "Star Wars: The Last Jedi" (2017), had appeared in over 80 films and was also a successful dialect coach.
Jack's fellow "Star Wars" actor Greg Grunberg said he was "devastated" to learn of his death, describing him as a "wonderful, talented, beloved gentleman".
"He is one of the kindest people I've ever worked with," Grunberg added.
Jack, who lived on a houseboat on the River Thames, had been "full of life", "funny, charming and a joy to be around. He was still working full-pelt, currently coaching on the new 'Batman'," his agent said.
The actor had been unable to see his wife and fellow dialect coach Gabrielle Rogers, who he was "madly in love with", because she was "stuck in quarantine in Australia, having just flown in from New Zealand last week," McCullough said.