He will begin his new role in October when Nicholas Kenyon leaves the BBC to become managing director of the Barbican.
As well as directing BBC Radio 3's editorial strategy, commissioning and scheduling policies, Wright is also responsible for four of the organization's performing groups: the BBC Concert Orchestra, the BBC Philharmonic, the BBC Symphony Orchestra and the BBC Singers.
Jenny Abramsky, director of BBC Radio and Music, said in a statement, "Roger is a brilliant Controller of Radio 3. I am delighted that he will bring his creativity to the BBC Proms. He will continue the work of Nicholas Kenyon who has been an inspired and innovative champion of the BBC Proms for 11 years."
According to the BBC statement, Wright has been the driving force behind Radio 3's composer-focused programming marathons such as "The Beethoven Experience" and "A Bach Christmas" as well as the network's decision to broadcast Wagner's entire 18-hour Ring cycle in one day.
Prior to working at Radio 3, Wright held the positions of Head of BBC Classical Music, executive producer and vice president for artists and repertoire at Deutsche Grammophon, artistic administrator of the Cleveland Orchestra, senior producer of the BBC Symphony Orchestra and director of the British Music Information Center.
The BBC Proms, which run for eight weeks, enter their 113th season this July.