Users of the service will have on-demand access to the shows, as well as other favourites such as 'South Park', 'Rugrats' and 'Pimp My Ride', when it launches later this autumn.
The television deal follows a similar one offering films from Viacom-owned Paramount Pictures and Dreamworks.
Other media companies who will be offering their content on BT Vision including BBC Worldwide, Sony BMG, Turner Broadcasting and Warner Music Group.
BT Vision will also show "near-live" FA Premier League matches from the 2007/2008 season.
The service will let people watch film, music and television when they want via a set-top box. The telecoms giant has teamed with Microsoft to develop the software and Philips, which has built the set-top box.
Dan Marks, chief executive of BT Vision, said: "This deal builds on our already strong relationship with the Viacom companies Paramount Pictures and Dreamworks. BT very much values the relationship with Viacom and looks forward to developing digital entertainment opportunities together in the future."
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