He was responsible for the BBC's production and broadcast technology strategy and investments and was also leading the work to digitise the BBC's archive.
Cheesbrough has worked on several projects at the BBC over the past seven years and has worked on technology-based programmes with corporations that include Fox, DSTV and ITV.
Before joining the BBC in 2000, Cheesbrough worked in IBM's media consulting division.
Cheesbrough is the latest high-profile departure from the BBC, following the exit of Tom Loosemore, who left his role as the web 2.0 project director in June to Ofcom and Matt Locke, former head of innovation, who left in March to join Channel 4.