Bradshaw moves from his current position as minister for health while Burnham has replaced Alan Johnson as health secretary in Gordon Brown’s far reaching Cabinet reshuffle.
The former BBC journalist and MP for Exeter will have responsibility for a department tasked with support and development of the advertising, design and media industries.
It also has crucial role to play in producing the final Digital Britain report, which is due to be published on June 16.
Burnham’s tenure has been a colourful one, rejecting the European Union directive allowing product placement on TV and indicating that football clubs should up the percentage of commercial revenue invested in the grassroots game.
He has also advocated self-regulation for digital marketing.
Brown has been busy reshuffling his Cabinet today after a number of recent high profile resignations including work and pensions secretary James Purnell and home secretary Jacqui Smith.