The media regulator today confirmed that Burns - currently chairman of financial chain Abbey - will replace the outgoing Luke Johnson from January 2010 after culture secretary Ben Bradshaw approved his three-year appointment.
Former ITV chief executive Richard Eyre was previously suggested as a potential candidate for the role, along with Lord Alli, co-founder of production company Planet 24.
The watchdog was reportedly keen to see a woman take on the job, but a range of candidates have ruled themselves out of the running.
Burns gained notoriety in the media industry after overseeing a government review of the BBC in late 2006 for the ten-year appraisal of the Royal Charter. The 65-year-old was also linked with the BBC chairman role in 2001 when Sir Christopher Bland moved on.
"I am delighted that we have been able to appoint someone of Terry Burns's calibre. He has an outstanding record of public service and a real depth of commercial expertise," said Ofcom chairman Colette Bowe.
"He will provide strong leadership at a time of considerable change in the broadcasting world. I would also like to pay tribute to Luke Johnson's tremendous contribution to Channel 4 in a period during which it has enjoyed considerable success."
Lord Burns added: "I am delighted to be joining Channel 4. This is a time of great change as we experience the impact of the rapid development of digital technology in the communications sector and Channel 4 has a very special and continuing role to play."
The first challenge facing Burns when he starts at Channel 4 will be overseeing the search for a new chief executive to replace the outgoing Andy Duncan.
He will further have to cope with the serious strategic challenges facing the broadcaster, including a £150m budget shortfall and the long-running discussions over a joint venture with BBC Worldwide.