The 65-year-old singer-songwriter started doing his weekly 'Theme Time Radio Hour' show for US satellite radio company XM Satellite Radio in May.
He plays an eclectic mix of his favourite songs according to a theme -- for example, 'Weather' included 'The Wind Cries Mary' by Jimi Hendrix and 'Keep on the Sunny Side' by the Carter Family.
Six of the shows will be broadcast on Radio 2 on consecutive evenings from Saturday December 23, before continuing on 6 Music on New Year's Eve and then on Friday nights from January 12.
Lesley Douglas, controller of Radio 2 and 6 Music, said: "Bob Dylan is a legendary figure and I'm sure these shows will be of great interest to our audience."
Dylan's presentation has drawn favourable American reviews, with Rolling Stone calling the show "revelatory" and Reuters describing him as "playful and spooky, topical and historical, eager to share his favourite stories and records".
Having sold almost 100m albums and still touring decades after his 1960s breakthrough with folk songs such as 'Blowing in the Wind', Dylan remains popular around the world.
Last September, BBC Two showed Martin Scorsese's 'No Direction Home', a documentary about Dylan's life and work.
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