The series, currently under the working title Bar Karma, marks Wright's first foray in TV and will focus on the same elements of user participation as in his games.
According to PaidContent, the show will involve an audience dictating all the storylines and plot developments before they are filmed.
Current TV has hired Albie Hecht, a former MTV Networks executive, and David Cohn, previously general manager of MTV2, to executive produce the show.
Premiering in early 2011, Bar Karma will involve users joining an online community to submit their story ideas for discussion with the producers.
The best concepts will be compiled into a formal episode proposal, and users can then vote on what aspects to keep before the finalised 30-minute episode is produced.
Current TV launched in 2005 under the leadership of former US vice president Al Gore and broadcasting executive Joel Hyatt.
The channel, which airs documentary, factual and entertainment programmes created by the industry and amateur filmmakers, is available on Sky and Virgin Media.