Keith Olbermann returns to television next Monday on cable network Current TV facing a formidable task: persuading viewers to tune into a virtually unknown channel to watch his new nightly show.

For Current TV, it's also an expensive gamble. But the channel—which was founded in 2005 by former Vice President Al Gore and Joel Hyatt—is counting on Mr. Olbermann to help transform the obscure public affairs start-up focused on user-generated content into a leading source of prime-time political commentary and news coverage in the...