Moore led its 2013 opening and first season and devoted more than 10 years to raising money for the new center.
In an e-mail statement, Moore told the Times that "upon completing our successful first season, it is clear there is a differing vision for the programming of the Wallis... I respect the board's vision just as they respected mine in the 14-year journey we undertook to create a new home for the arts."
"Lou did a fantastic job of getting us to where we are," board chairman Jerry Magnin told the Times, also saying that running the center following its opening required "totally different responsibilities. The pressures on both sides change."
Moore previously served as the managing director of the Geffen Playhouse, working closely with the late Gil Cates.
Patricia Wolff, who has served as the company's artistic associate, has assumed the role of interim artistic director.
Visit thewallis.org for more information.