Peter Capaldi, 55, is replacing outgoing lead Matt Smith.
He is best known for his role as foul-mouthed spin-doctor Malcolm Tucker in the BBC series The Thick of It.
“It’s so wonderful not to keep this secret any longer, but it’s been so fantastic,” Peter Capaldi said after the news was revealed on a live BBC One show.
The actor had been the bookmakers’ favorite to take on the role, with betting on him becoming the next Doctor suspended on Friday.
It is not the first time Peter Capaldi has appeared on the show – he played Roman merchant Caecilius in 2008 Doctor Who adventure The Fires of Pompeii.
At 55, Peter Capaldi is the same age as William Hartnell when he was cast in the role as the first Doctor in 1963.
“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. I can’t wait to get started,” he said.
Steven Moffat, the show’s lead writer and executive producer, said casting Peter Capaldi as the Doctor was an “incendiary combination”.
“One of the most talented actors of his generation is about to play the best part on television.”
Steve Moffat said Peter Capaldi had been cast after a secret audition at his house.
“We made a home video of [Peter Capaldi] being the doctor and I showed it around and everyone said <<yes, that’s the Doctor>>.”
Steve Moffat added the actor had “briefly flicked through my mind” the last time he was casting the role, but he did not think he was right for the part, however “now that moment has arrived”.
Peter Capaldi said he downloaded old Doctor Who scripts from the internet and practiced the lines in front of a mirror to prepare for the audition.
Outgoing Doctor Matt Smith welcomed Peter Capaldi’s casting, who pre-recorded a message for the new Time Lord.
“I wish my successor all the best and say good luck and good on you for getting it, because I know he’s both a huge fan of the show and a really nice guy,” Matt Smith said.
“The casting made me ready excited and as a fan I think it’s a canny choice. If I had to pick someone, I’d pick him because I think he’s great. I’m excited because I know what’s coming and he’s going to have a blast.”
Peter Capaldi will film his first scenes on the series this autumn.
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