LONDON — Britain’s National Theatre on Tuesday named stage director and former actor Rufus Norris as its next chief. He is the first actor since Laurence Olivier to lead Britain’s biggest and most influential theater company.

Norris will take over in April 2015 from Nicholas Hytner, who has led the state-subsidized company through a decade of commercial and critical successes, including Broadway runs for shows such as “One Man, Two Guvnors” and “War Horse.”

Last year the National’s shows played to 3.6 million people around the world — at its London home, on tour and in live cinema broadcasts — and it took in 87 million pounds ($139 million).

Norris acknowledged nerves about the scale of the job, but said he would approach it “with gusto” and continue efforts begun under Hytner to attract younger and more diverse audiences and artistic collaborators.

Norris, 48, trained at the Royal Academy of Dramatic Art and worked as an actor — “I wasn’t quite as good as Olivier” — before making a name as a bold and versatile director of plays, musicals and opera.

He spent five years as associate director of the innovative Young Vic in London, and has directed several shows at the National, including James Baldwin’s “The Amen Corner” and David Eldridge’s “Market Boy.”

His work on Broadway includes a 2008 production of “Les Liaisons Dangereuses” that received five Tony Award nominations.

Norris created the opera “Dr Dee” with Blur frontman Damon Albarn, and made his filmmaking debut in 2012 with “Broken.”

Norris is currently working on a movie adaptation of “London Road,” a musical he directed at the National about a neighborhood traumatized by a serial killer. But he acknowledged that his film career will have to take a back seat to running the theater.

“I’d like to think you can do this job and direct a movie a year alongside it — but clearly that’s not the case,” he said. “It’s an enormous job.”

High-profile directors including Sam Mendes and Kenneth Branagh were rumored to be in the running for British theater’s biggest job. Hytner said the most important quality needed — even more than experience — was “appetite.”

“Rufus has the appetite, as well as the talent,” he said.