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Dr Shah, 71, previously held a series of roles at the BBC, including as its head of current affairs. In a statement, he said he was "delighted" to have been named the government's preferred candidate. A BBC spokesperson said: "We welcome the announcement that Samir Shah has been selected as the government's preferred candidate to take up the role of BBC chair and look forward to him joining the board once the formal process has been completed."
His selection marks a sea change, as it means there will now be a journalist at the top of the BBC.
Dr Shah has worked in TV for more than 40 years, starting at London Weekend Television in 1979.
Since then, he has held positions as the BBC's head of television current affairs, and later went on to head the corporation's political journalism across radio and television.
In 2007, he was appointed as a non-executive director on the BBC Board.
Dr Shah is currently chief executive of Juniper, an independent production company, which supplies programmes to the BBC, as well as other organisations including Channel 4, Netflix and National Geographic.
The announcement that Dr Shah was the preferred candidate was broadly welcomed on social media, with broadcaster Andrew Neil describing him as "superb" choice.