The corporation's commercial arm BBC Worldwide secured the deal with Apple, which will offer a selection of BBC shows at iTunes' standard UK rate of£1.89 an episode.
The BBC is the first UK broadcaster to strike such a deal.
Viewers will be able to watch the shows on Macs, PCs, video iPods, iPhone and Apple TV.
The BBC will offer mostly archived series, though some recently-aired shows such as Ashes to Ashes will be on iTunes after their seven-day catch-up window on BBC iPlayer.
Other shows on offer include Life on Mars, Torchwood, Little Britain, Spooks, The Catherine Tate Show 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.