The re-election comes just a few months after the organisation investigated and dismissed a sexual harassment allegation against him.
Bailey is the first cinematographer to hold the position of Academy president, which boasts of more than 9,000 members, the organisation said in a release.
His credits include "Ordinary People", "American Gigolo", "The Big Chill", "Groundhog Day" and "As Good as It Gets".
Academy board members may serve up to three consecutive three-year terms, while officers serve one-year terms, with a maximum of four consecutive years in any one office.
The Academy recently invited more than 900 new members, including Indian actors such as Shah Rukh Khan, Tabu, Madhuri Dixit and Naseeruddin Shah, to increase the representation of women and minorities by 2020.