Radcliffe, identified as one of Marketing's Power 100: Next Generation in 2006, joined the broadcaster in 2000. He was made head of marketing for the core C4 brand in 2005 following the launch of More4.
Radcliffe will oversee marketing across C4's portfolio. He will take on the research and airtime management duties formerly handled by Cochrane, but not press and communications. He will also assume the responsibilities of head of digital channels Cameron Saunders, who is leaving C4 and will not be replaced.
A spokesman said C4 had yet to decide whether to replace Cochrane.
C4 is in the midst of a cost-cutting drive to save £100m in the next two years. It has closed its third-party advertising business and withdrawn plans to launch into digital radio.