Sam Mendes, veteran film and theater producer who is heading up the musical for DreamWorks, said he will name a composer soon.
Although Moore received a Tony nomination for "Avenue Q," "Shrek" will be the director's biggest undertaking to date.
"There's a supreme challenge in bringing an animated world to the stage and making it theatrical. But what's so wonderful about 'Shrek' is that anarchic attitude placed in a fairy tale world that I think will thrive onstage," he said.
"Shrek" is Lindsay-Abaire's first Broadway play after success on off-Broadway productions of "Kimberly Akimbo" and "Fuddy Meers."
The musical tentatively is scheduled to debut in 2006 for an out-of-town showing followed by a move to Broadway, the Times said.