Cowell will be joined on the judges' panel by Antonio "L.A." Reid, former chairman of Island Def Jam Music, when the show premieres in September.
"The X Factor" is based on Cowell's British-born hit series and debuting on Fox this fall. At stake is a $5 million recording contract.
Those invited to the booths to sing must be at least 12 years old and can be solo artists or vocal groups. Each audition will be sent to the show's producers, and those selected will take part in callbacks.
The decision has not been made about who the third judge will be, but Cowell said that Black Eyed Peas singer Fergie has come up in discussions.
"Her name was put forward, but like with a lot of other people we've spoken to, we have to check out everyone's availability," he said. "There's a lot of time you have to put into this show. This is not a two-day-a-week process. When you're mentoring the contestants, you're working 5, 6 days a week."
Cowell hopes his show will produce audition moments that go viral.
"You want a moment where something magical happens in the audition room, and then outside of people watching the show, they're interested in the clip, and I'm always very, very aware of that," he said.
"You look at what happened to Rebecca (Black)," he continued, referring to the 13-year-old Internet sensation of the song "Friday." "She's gonna be laughing all the way to the bank. This would never have happened 10 years ago. Now she's known all over the world."
So far, Cowell said he and producers are pleased with the audition process for the show. Thousands turned out in Miami on Thursday, and Gloria Estefan made an appearance to get the crowd even more excited.