The Hour and The Thick Of It actor, 55, will replace Matt Smith as the famous time travelling hero.
The Scot will be the 12th Doctor in BBC1's hit sci-fi drama after Matt revealed he was quitting the show after four years.
The announcement was made in tonight's (August 4) live show Doctor Who Live: The Next Doctor, which was hosted by Zoë Ball.
Peter, a lifelong Doctor Who fan, admitted he had found it difficult keeping his new job a secret.
He said: "It's so wonderful not to keep this secret any longer.
"For a while I couldn't tell my daughter. She was reading the rumours on the internet and getting upset that they weren't mentioning me."
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