Deadline reports that the drama will be based on Barton Gellman's book Angler: The Cheney Vice Presidency and the documentary The Dark Side.
The show is expected to follow Cheney's rise in Washington from his time in the Nixon administration up to his two terms as Vice-President for George W. Bush.
The drama's producers claimed that it will examine Cheney's "single-minded pursuit of enhanced power for the Presidency [that] was unprecedented in the nation's history".
Rick Cleveland, who has previously worked on Nurse Jackie, Six Feet Under and The West Wing, is penning the script. The show will be produced by Paula Weinstein, whose credits include Recount, Blood Diamond and Truman.
HBO is also currently developing shows including a political drama from Morgan Spurlock, a series about a Soviet spy and a comedy called Veep from Armando Iannucci. Meanwhile, Julianne Moore recently signed up to play Sarah Palin in an HBO movie about John McCain's presidential campaign.