The deal with Apple will see the BBC's commercial arm offer programmes at £1.89 per episode and will allow users to watch the shows on a PC or Mac, video-enabled iPod, iPhone or Apple TV.
Other series to be made available via iTunes include Little Britain, Spooks and Robin Hood.
"We want to give audiences a wide variety of options on how and where to view their favourite BBC shows," said Simon Danker, director of digital media at BBC Worldwide.
"With more people choosing to watch TV shows on their iPods, fans of series such as The Mighty Boosh and The Catherine Tate Show can enjoy those shows wherever they are."
Recently broadcast programmes that have been made available on BBC iPlayer will also be available for purchase via the iTunes store.
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