The Zygos Partnership has begun the search and it is understood that Ofcom want the head hunter to consider candidates from both media and non-media backgrounds.
Recruitment advertising for the role is expected next month.
Johnson (pictured), the entrepreneur and former Pizza Express owner, was a surprise to many when he was appointed to the chairmanship by then Ofcom chief executive Stephen Carter in January 2004.
In July 2006, Johnson was then reappointed for an additional three years.
Previous chairmen have included Sir Richard Attenborough and Sir Michael Bishop.
The search comes at a time when a joint venture between the broadcaster and BBC Worldwide is expected to be announced.
The tie-up will help to plug a £150m funding gap Channel 4 will face from 2012.
Smith says the deal is likely to be inked within weeks and will see it take over parts of Channel 4’s divisions including advertising sales.