The scheme, called the Radio Amnesty, will be supported by a marketing campaign funded by the radio industry and coincides with the scheduling of exclusive digital coverage of the Fifa World Cup and other sporting and musical events this summer.
From this Saturday (22 May), consumers will be able to get discounts on digital radios from Alba, Bush, MagicBox, Panasonic, Philips, Proline, Pure, Roberts and Sony at participating retailers, which include Argos, Comet, John Lewis and Tesco, as well as independent stores.
The offer will run until 26 June. All analogue sets handed in will either be reconditioned and donated to charities working in southern Africa, or recycled if they are beyond repair.
The on-air promotions for the scheme, created by Abbott Mead Vickers BBDO, are voiced by Stephen Fry, Gaby Roslin and Noddy Holder. They will be played on commercial radio stations such as Classic FM and Absolute Radio, as well as national and local BBC stations.
Ford Ennals, chief executive of Digital Radio UK, the company responsible for promoting digital radio in the UK, said: 'The Radio Amnesty gives consumers even more reasons to get digital radio. This is an amazing summer of exclusive sports and music on digital radio and a great opportunity to support children's charities.'
Andrew Harrison, chief executive of the commercial radio trade body RadioCentre, said: 'The Radio Amnesty is a terrific scheme which will see many more listeners discovering the benefits of digital radio.
"The scheme has the full support of all the major commercial radio groups, including Global, Bauer, GMG Radio, Absolute Radio and UTV Radio, as well as exclusive-to-digital services, such as Planet Rock and NME, Jazz FM and Panjab Radio, which are donating significant airtime to the promotion to ensure that our listeners know about this great opportunity."
The offer has been developed by the BBC with the support of Digital Radio UK, commercial stations, set manufacturers and retailers.
More than a third of adults (34.5%) now have a DAB set at home, according to the Rajar radio audience report for the first quarter of 2010.