The move means Moore will have a different job for a fourth successive year, though this is his first role as head coach.
The 36-year-old previously worked at the Dallas Cowboys between 2018 and 2022 – serving as offensive coordinator the last of those years, before similar roles at the Los Angeles Chargers in 2023 and the Eagles last season.
“He is an outstanding communicator with the ability to lead people and has a clear vision for this football team,” said Saints general manager Mickey Loomis.
Team owner Gayle Benson added: “Through the search process, it became clear that Kellen is the right person to help us re-establish a winning programme and culture that our fans are accustomed to and have come to expect.”
The Saints have missed out on the play-offs the last four seasons and have reached just one NFC Conference final since winning the Super Bowl in 2010.
The Eagles beat the Kansas City Chiefs 40-22 in New Orleans on Sunday to deny them an unprecedented third straight Super Bowl.