John Doyle, the Broadway director who’s staging the upcoming revival of “The Color Purple” and who won a Tony Award for his production of “Sweeney Todd,” has been named the new artistic director at Off Broadway’s Classic Stage Company.

He’ll step into a post to be vacated at the end of the 2015-16 season by Brian Kulick, who’s been in the job for 12 seasons. Doyle, who’s made a name for himself with pared-down revivals of musicals including “Sweeney,” “Company” and the upcoming “Color Purple” (which won raves in its premiere in London), has worked at CSC previously, staging scaled-back versions of “Passion” (another musical by “Sweeney” and “Company” songsmith Stephen Sondheim) and “Allegro.” Later this season he’ll helm “Peer Gynt” there. He’s been associate director of the company since 2013.

During Kulick’s tenure at Classic Stage Company, the forty-eight-year-old downtown organization has become known for its starry revivals of well-known titles from the canon of classical and modern drama. Productions of Chekhov plays — starring the likes of Ethan Hawke, Dianne Wiest, Maggie Gyllenhaal and Peter Sarsgaard — have gained particular notice; last season the company staged Turgenev’s “A Month in the Country” with Peter Dinklage and Taylor Schilling.

CSC also originated David Ives’ “Venus in Fur,” which went on to a successful Broadway run and launched the career of Nina Arianda, who won a Tony for her work in the show.

After the 2015-16 season, Kulick — who will direct productions of “Mother Courage and Her Children” and “Nathan the Wise” at CSC in the coming months — plans to spend more time directing independently, as well as continue his teaching work at Columbia University. Doyle, whose revival of “The Color Purple” opens on Broadway in December, takes the reins at CSC in July.