The television network announced the new role change during a Sunday evening broadcast. The new Doctor's identity had been the subject of speculation for quite some time.
Capaldi is the 12th actor to play the Doctor, a galaxy-hopping Time Lord who travels in the Tardis, a time machine shaped like an old-fashioned British police telephone booth.
Capaldi, a fan of the show since childhood, said that "being asked to play the Doctor is an amazing privilege."
"Like the Doctor himself I find myself in a state of utter terror and delight," he said.
Capaldi has a long list of movie, television and stage credits. He is best known as venom-spitting political fixer Malcolm Tucker in the sitcom "The Thick of It" and its film spin-off, "In the Loop."
"Doctor Who" was first broadcast in 1963 and is now one of the BBC's most popular programs, both in Britain and abroad.
The part of the Doctor has been played by Matt Smith since 2010. He will leave after a November episode to mark the show's 50th anniversary and a Christmas special that will see him regenerate into Capaldi. Capaldi's first full episode will air next year.
The Associated Press contributed to this report.