Lord Burns was until January 2016 the chairman of Channel 4, having served for six years at the public service broadcaster.
He has also served as chairman of a number of private and public-sector organisations, including Marks & Spencer, Santander UK, Welsh Water, National Lottery Commission and The Royal Academy of Music.
From 2004 to 2006, Lord Burns was independent adviser to the secretary of State on the BBC Charter Review.
Lord Burns said: “I am very pleased to have the opportunity to take on this role at an important time for Ofcom. The UK communications sector provides essential services to everyone in the UK and is critical to the future success of the economy.”
Sharon White will continue as the chief executive of Ofcom.
Dame Patricia Hodgson will be leaving at the end of the year, after serving the telecom regulator as chairman and deputy chairman over the past six years.