The first series of six 30-minute episodes of the show, which made stars of Rik Mayall, Adrian Edmonson and Nigel Planer when it aired in 1982, are now available on the digital music and video store for£1.89 per episode.
The second and final series will also be made available in the coming weeks.
When BBC Worldwide first made content available on the site, it concentrated largely on contemporary hits such as Robin Hood, The Mighty Boosh, Little Britain and Spooks.
The oldest shows available were the first series of The League of Gentlemen and documentary series Planets, both of which were broadcast in 1999.
BBC Worldwide said it was encouraged to release the full episodes after clips of the show proved a hit on its YouTube and MySpace video channels.
A clip of Edmondson's punk character Vyvyan losing his head when he looks out of a moving train has attracted 20,455 views on MySpace.
BBC Worldwide digital media director Simon Danker said: "Making the series available on iTunes will bring it to a whole new audience, while existing fans can relive their 80's memories with a show that literally blasted its way on to the screens.”
The videos will be viewable on Mac or PC, iPod with video, iPhone or Apple TV.
* BBCW is also making its landmark environmental series Planet Earth available on the UK iTunes store. The 11 x 50-minute series can be downloaded for£17.99 or£1.89 per episode.
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