"We had the time of our lives collaborating with Lucasfilm and Disney on 'The Last Jedi, '" Johnson and Bergman said in a joint statement.
"Star Wars: The Last Jedi" begins where "The Force Awakens" left off, with Rey (Daisy Ridley) having tracked down Luke Skywalker.
Disney chairman-CEO Bob Iger announced the "Star Wars" news during the company's quarterly earnings call.
When Colin Trevorrow was booted off Star Wars: Episode IX, a lot of people were surprised that Last Jedi director Rian Johnson wasn't hired as his replacement.
Disney said no release dates have been set for the new trilogy.
He effectively said, "Do not worry about these numbers, instead look at this" in announcing there will be an entirely new Star Wars trilogy after Disney finishes the one it's now working on.
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Lucasfilm president Kathleen Kennedy said: "We all loved working with Rian on The Last Jedi".
That's high praise indeed when you consider Kennedy has butted heads with other directors who have contributed to Star Wars in recent years. The next chapter of the new trilogy, The Last Jedi, arrives this December, and J.J. Abrams is beginning pre-production on the conclusion for 2019.
Johnson was brought on to write and direct the second film in Disney's rebooted trilogy of the Skywalker stories, which George Lucas first brought to screen in 1977.
The most interesting thing about this new trio of films is that Lucasfilm has specifically stated that it will not deal with the Skywalker family.
Disney is also making three standalone Star Wars films, including last year's Rogue One and next year's Solo: A Star Wars Story, following the origins of the charming roguish smuggler Han Solo, made famous by Harrison Ford in the franchise.