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.
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Online: www.nationaltheatre.org.uk
Jill Lawless can be reached at http://Twitter.com/JillLawless