Rapier won the four-year contract in a final shoot-out against Proximity London. Partners Andrews Aldridge and OgilvyOne were knocked out at an earlier stage.
The agency will work alongside Digital UK's ad agency, Abbott Mead Vickers BBDO, and its media agency, MediaCom, to help convert the remaining non-digital viewers in the UK.
The timetable for switch-over was announced in September by Tessa Jowell, the secretary of state for culture, media and sport. It will take place region by region, beginning with the Border TV region, between 2008 and 2012.
Rapier's first task will be to create leaflets for households in the Border TV, West Country and Wales regions, for delivery in spring.
Jane Ostler, Digital UK's head of marketing, said: "Direct communications to every UK household are crucial so that people understand what they need to do to prepare for digital switchover. Rapier came up with some insightful ways to complement our information campaign."
Jonathan Stead, the Rapier chief executive, said: "This challenging role is central to communicating the switch-over process, which will benefit every household in the UK.
"We are looking forward to being part of this momentous project."
The government has pledged to make digital TV available via an aerial to all households in the UK. Currently, one in four UK households is unable to receive the full range of digital TV services available through an aerial.
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