Disney will pay about half in cash and half in stock, issuing 40 million Disney shares in the transaction.
The deal follows Disney's acquisitions of Pixar studios for $7.4bn in 2006 and Marvel comics for $4.2bn in 2009.
"Our valuation of Lucasfilm is roughly comparable to the value we placed on Marvel when we announced that acquisition in 2009," Disney said, adding that the valuation was almost entirely driven by the Star Wars franchise.
George Lucas launched Lucasfilm in 1971 and the first Star Wars film was released in 1977.
"For the past 35 years, one of my greatest pleasures has been to see Star Wars passed from one generation to the next," Mr Lucas said.
"I've always believed that Star Wars could live beyond me, and I thought it was important to set up the transition during my lifetime."
Mr Lucas will continue as a creative consultant.
Kathleen Kennedy, currently co-chairman of Lucasfilm, will become president of the firm and will be the executive producer on the new Star Wars films.
When the later Star Wars films were released in the 1990s and 2000s, although they did well at the box office, they were generally not well-received by fans.
But Josh Dickey, film editor at Variety magazine in LA, said that Disney was a "great fit" to update Star Wars.
"They're so good at branding and brands. They're so good at working with existing intellectual property and making it resonate with fans and marketing it very well," he told BBC World Service radio.
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