Morley had been touted as part of the new type of mobile specialists moving into the outdoor industry as digital screens with dynamic capability continue to become more important.
Until April 2014, Morley has been head of Motorola at Google in the UK and Ireland after making a name for himself as the international vice president of marketing at Motorola.
He replaced Matthew Dearden, the previous UK CEO, who was promoted to president of Clear Channel Europe and chair of Clear Channel UK.
Campaign understands Morley's exit was under mutual consent. Cochrane is well known to the company, having worked in various roles for 14 years, including as chief finance officer.
The change in leadership comes at an important time for the outdoor media owner, which is battling to retain TfL's £500 million London bus shelter contract, an account it has held for the last 10 years.