Zudeo users will be able to download copies of Red Dwarf
The move follows a deal between the commercial arm of the organisation, BBC Worldwide, and technology firm Azureus.
The agreement means that users of Azureus' Zudeo software in the US can download titles such as Little Britain.
Until now, most BBC programmes found on peer-to-peer file-sharing networks have been illegal copies.
Beth Clearfield, vice president of program management and digital media at BBC Worldwide, said that the agreement was part of a drive to reach the largest audience possible.
"We are very excited to partner with Azureus and make our content available through this revolutionary distribution model," she said.
Azureus is best known for developing a BitTorrent client, or program, that allows large media files to be easily shared over the internet. The program has been downloaded more than 130 million times.
Earlier this month the company launched a video sharing site similar to YouTube, codenamed Zudeo. The site allows users to upload and view content.
However, in contrast to most video sharing sites, Zudeo offers high definition videos. Users must also download a program to access and upload content.
The new deal means that users of the software will be able to download high-quality versions of BBC programmes, including Red Dwarf, Doctor Who and the League of Gentleman. Classic series such as Fawlty Towers will also be available through a BBC "channel".
The titles will be protected by digital rights management software to prevent the programmes being traded illegally on the internet.
"This will be a very different experience from traditional file-sharing networks," said Gilles BianRosa, CEO of Azureus.
Users will also be able to link to programmes from blogs, social networks and fansites.
"If you have Zudeo running it will take you to that programme; and if you don't, it will suggest you install it, like the first time you download a flash movie," said Mr BianRosa.
"Once you have watched a show, you can rate it, comment on it and recommend it to a friend."
Mr BianRosa believes the cult status of many BBC programmes will make these features appealing to Zudeo users.
File-sharing is often associated with illegal distribution of copyrighted content. But in recent months a number of networks have tried to shake off this old image.
BitTorrent, the company behind the original file-sharing software of the same name, has recently signed a number of deals with content providers, such as 20th Century Fox, in a bid to become a legitimate download service.
Earlier this year, Sharman Networks, the owners of Kazaa, did similar deals. Kazaa uses advertising to provide content for free.
No pricing structure for the BBC content on Zudeo has been revealed.
Azureus is expected to announce other partnerships in the New Year.