The agency won the business following a pitch against Agency Republic and Cuba.
The station is set to relaunch the channel next year with a new programming schedule containing more of a focus on entertainment. The channel held the pitch in a bid to find an agency partner that could produce a campaign to compliment this new positioning.
Leith London's new work will include TV commercials running from February.
Jeremy Pyne, the managing director of Leith London, said: "The Biography Channel deserves a campaign that communicates its core proposition in a distinctive way."
The Biography Channel's sister channel, The History Channel, is also talking to agencies about its ad account.