The pair will appear in Darren Aronofsky's biblical adaptation, reports Deadline.
They will star alongside Russell Crowe, Jennifer Connelly and Saoirse Ronan in the Paramount Pictures movie.
The film is a close retelling of the story of Noah and his escape from the flood carrying two of each animal.
Aronofsky and Ari Handel wrote the script, which was revised by Academy Award-nominated screenwriter John Logan (Gladiator, Hugo).
Booth, who will star opposite Hailee Steinfeld in the forthcoming Romeo and Juliet, will play Noah's son Shem.
Logan Lerman (The Perks of Being a Wallflower) will appear as another son, Ham.