John Malkovich and Joan Allen headlined the original, 1987 production, which ran off-Broadway before transferring to Broadway.
"Burn This tells the story of four New Yorkers whose lives are uprooted by a young dancer's accidental death," a press release noted.
"Set in downtown New York in the raw and gritty 1980s, the combustible drama explores the spiritual and emotional isolation of the dangerous, sexy, raw and demanding Pale and the modern dancer Anna, and their tempestuous relationship after the two iconoclasts are brought together in the wake of a life-changing personal tragedy."
The theater where it will play, additional casting and the design team will be announced shortly, the producers said.
Driver's Broadway credits include "Man and Boy" with Frank Langella and "Mrs. Warren's Profession" with Cherry Jones.
He can now be seen playing Darth Vader's grandson Kylo Ren in "The Last Jedi."
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