Johnson, who, as the chairman of Signature Restaurants, owns The Ivy, takes over the £67,500-a-year post from Vanni Treves. He beat a field of candidates including the fashion retailer Stuart Rose, the chief executive of Guardian Media Group, Bob Phillis, and the former president of Coca-Cola UK, Penny Hughes, who was widely tipped to get the job.
Johnson, 42, started his career at DDB, then worked at TV-am before joining Kleinwort Benson as a media analyst. He has had a colourful career with most of his business interests centred on restaurants, including the Belgo and Bierodrome chains.
In 1997, Johnson backed the relaunch of the Sunday Business. He is the son of the journalist Paul Johnson and a business columnist for The Sunday Telegraph.
The appointment was made by the chairman of Ofcom, Lord Currie, its deputy chairman, Richard Hooper, the chief executive, Stephen Carter, and the former Independent Television Commission chairman, Sir Robin Biggam, and was approved by the culture secretary, Tessa Jowell.
Currie said: "Luke combines an outstanding commercial and strategic track record with a passion for public service broadcasting and Channel 4."
Mark Thompson, the chief executive of Channel 4, said: "I'm pleased to welcome Luke and look forward to forming a strong working relationship with him."