Written by Katori Hall, The Mountaintop depicts the civil rights leader on the night before his 1968 assassination.
Producers Jean Doumanian and Sonia Friedman said they were “thrilled” and “honoured” that the 62-year-old Pulp Fiction star had agreed to appear.
Performances will begin on 22 September at New York’s Bernard B Jacobs Theatre.
It had been reported that Halle Berry would co-star in the production as a maid at the Memphis hotel where Dr King stayed prior to his death at the age of 39.
But producers said the actress would not be appearing “due to child custody issues”. The Oscar-winning star is currently involved in a custody battle with her ex-boyfriend, Gabriel Aubry.
David Harewood played the lead role in the London production of The Mountaintop, which was named best new play at last year’s Laurence Olivier awards.
Jackson was Oscar nominated for his role in Pulp Fiction and will shortly be seen in a cameo role in comic book fantasy Thor.