Randall had earlier this week announced his intention to step down from his BBC job by the end of the year and fish for a move back into print journalism.
The Telegraph regards his signing as a coup, not least because he is a former City editor of The Times, as well as editor of Sunday Business, now The Business.
Telegraph editor Martin Newland said: "Jeff is a marvellous acquisition. He talks and writes about complex financial matters in a language people understand. And he does it with extraordinary authority."
Randall will continue to do work for the BBC, including hosting 'Weekend Business', the Sunday radio show on Radio Five Live.
"I have had a great time at the BBC, but the chance to write a column in Britain's best-read quality newspaper is just to great to say no to. I can't wait to get started," Randall said.
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