Norman, a former Conservative MP, will replace Michael Grade as non-executive chairman from January.
He says the job is “an irresistible challenge”, adding the broadcaster is “a great brand” that is “facing an imperative for change: the challenge of adapting to compete in a fragmented digital media world”.
His appointment follows months of speculation over the replacement for Grade, who is also stepping down as chief executive.
Former Channel 4 chairman Sir Michael Bishop and Sir Crispin Davis, a former Reed Elsevier chief executive, were just two names to have been linked with the post.
The hire also clears the way for the broadcaster to resume its search for a new chief executive.
John Cresswell, the company’s chief operating officer, is to take on the job on an interim basis in January when Grade leaves.
Negotiations with former BskyB chief Tony Ball broke down earlier this year because of a disagreement over pay and the future of the chairmanship.