The website - which covers everything from Morecambe and Wiseto Buffy The Vampire Slayer- will close on 15 July, when much of material will be removed from servers and effectively disappear forever.
The corporation said the Cult site did not offer "sufficient distinctive public value" and said other websites already covered the same ground.
But one show has survived the cull - Doctor Whohas morphed into its own website after the success of the shows latest incarnation on BBC1.
The decision met scathing criticism from the site's devotees - which numbered more than 700,000 people last month.
One user commented on the site's chat forum: "This decision ranks alongside throwing out old recordings and closing down the Radiophonic Workshop in terms of short-term, short-sighted, bone-headed stupidity."