Current CEO Ian Ayre will be departing his role at the end of February as he takes up a position at German second-division side 1860 Munich.
Ayre decided to depart three months ahead of schedule to become German 1860 Munich's general manager.
Moore, who was born on Merseyside, will join the club in the summer when he leaves his role as chief competition officer at EA Sports' competitive gaming division.
EA confirmed the news in a post on its own website from CEO Andrew Wilson.
"Peter has been with us here at EA for nearly 10 years, and I consider myself privileged to have had the opportunity to work alongside him for that entire journey," he said. "If you've seen him on stage, or follow him on Twitter, or have ever read an interview with him, you will have a sense of Peter's wit and charisma. What you should also know is that he is an unbelievable teammate, a tireless leader for our people, and his deep appreciation for great games and the passionate players in our communities is unwavering."
Wilson added that Moore will continue leading EA's competitive gaming business for at least a period of several weeks. It's unclear how soon his successor will be named.