The deal has been negotiated by Total Media and RadioWorks. The three-part weekly series will be broadcast on Absolute Radio from Sunday. It will also be available on a V&A branded section of the Absolute Radio website.
Simon Kilby, Absolute Radio's commercial director, said the deal was the kind of project it could now offer advertisers following the relaxation of Ofcom's Broadcast Code.
He said: "Our bespoke radio show for the David Bowie at the V&A is a superb example of the new types of products we are able to offer our commercial partners."
The series is the second of Absolute Radio's ad-funded programming, following their new comedy show 'A Design for Life'.
The show will be presented by award winning comedian and Bowie fan, Tim Minchin, and friends and musicians who have been part of his past six decades will recount Bowie's story.
Contributors, including childhood friend and artist George Underwood, and guitarist John "Hutch" Hutchinson will draw on the memorabilia, lyrics and photos from the V&A exhibition, which was launched following the release of Bowie's new album 'The Next Day'. The album was released last month and is Bowie's first release in a decade.
The documentary will not only span Bowie's music career, but will also explore his acting and his role as a producer for the likes of Iggy Pop and Ian Hunter, and his fascination with technology and the internet.
The three hour-long programmes will broadcast on Sunday 7th, 14th and 21st April at 7pm. It will be accompanied by a series of short online films containing additional material and interviews.Follow @chloeellaSmith