Rufus Norris is to succeed Sir Nicholas Hytner as director of the National Theatre from April 2015.
"In setting out to find a new director for the National Theatre, the board looked for an individual with a creative reputation that would command the respect and support of British theatre, and with the generosity of spirit that has characterised Nick Hytner's period as director," explained chairman John Makinson.
"Rufus Norris has both those qualities in abundance. He is an exciting choice, someone who will build on the National Theatre's present reputation as one of the most admired and innovative performing arts organisations in the world. We are fortunate that he has chosen to join us.
"I should like to thank all my board colleagues, and in particular my fellow members of the succession committee, for the energy and insight that they have brought to this selection process."
Nicholas Hytner added: "I could not be more delighted that the board of the National Theatre has appointed Rufus Norris as the National's next director. He has been a superb associate director for the last two years, actively involved in repertoire planning, and delivering a series of outstanding productions.
"His work as a director is always searching, deeply considered and adventurous and I have no doubt he will bring these qualities to the running of the National. His appointment will be welcomed with great excitement both within the National and in the theatre at large."
Rufus Norris said: "This appointment is a great honour and I am thrilled at the prospect and challenge of leading this exceptional organisation, where it has been a privilege to work under the inspirational leadership of Nick Hytner.
"I am tremendously grateful to the board of the National Theatre for their support.
"The National is an extraordinary place, full of extraordinary people, and I look forward with relish to the task ahead – that being to fill our theatres with the most exciting, accessible and ground-breaking work our unique and broad community of artists has to offer."
Next week the Queen and the Duke of Edinburgh are due to visit the National Theatre as the company celebrates its 50th anniversary.