Lord Burns joins the Channel 4 Board as chairman-designate and takes up Johnson’s position on 27 January.
One of his first challenges will be to find a new chief executive to replace Andy Duncan.
Duncan is set to leave at the end of the year and speculation has put a number of names in the frame as possible successors, including ITV director of TV, channels and online Peter Fincham, ITV director of strategy and development Carolyn Fairbairn and BBC chief operating officer Caroline Thomson.
Lord Burns will also have to help find a solution to the broadcaster’s funding problems as the once potential tie-up with BBC Worldwide now seems unlikely.
Lord Burns is also a chairman of Welsh Water and the Royal Academy of Music. He is a former chief economic advisor and permanent secretary to the Treasury and former chairman of Marks & Spencer and Independent advisor to the Secretary of State for the BBC Charter Review.
Ofcom chairman Colette Bowe says: “Terry Burns has an outstanding record of public service and a real depth of commercial expertise. He will provide strong leadership at a time of considerable change in the broadcasting world.