The channel bid for the rights at the LA Screenings for the show, which is produced by Red Arrow Entertainment's UK arm for NBC, reported Digital Spy.
The series is loosely based on Homer's epic poem of the same name, and stars Anna Friel, Peter Facinelli and Jake Robinson.
Peter Horton (Grey's Anatomy), Adam Armus (Heroes) and Kay Foster (The Following) are the show's creators.
'Odyssey' follows the story of a team of US soldiers led by Friel who kill a key Al-Qaeda commander in a gunfight with jihadists, before discovering a major US corporation is funding the terrorists.