He replaces David Kerr who quit in July to become the director of broadcast at British Eurosport.
Thompson has been the head of new media development and sports news at the public broadcaster since 2001, responsible for the BBC Sport website and streamed video coverage of events such as the Olympics and Wimbledon.
He will start in February and report to C4 director of programmes, Kevin Lygo.
Free-to-air broadcaster Channel 4 recently lost its biggest contract to Sky Sports for England’s home cricket Tests.
