The presenters said they hoped the horse will run its first race during the next few months, during an interview for tonight's Jonathan Ross Show on ITV.
Declan Donnelly said: "We had to name the horse because obviously it wasn't named for racing, so we had a chat with Simon. His first suggestion was 'I think we should call him Simon'."
They eventually settled on the name It's A Yes From Me – a reference to a phrase often used by panelists on Cowell's talent shows.
Ant McPartlin added: "It hopefully might run in the summer."
Ant and Dec previously owned another horse, which they recently sold.
They also told Ross they have had to insure themselves as a double act, so the other would get a payout if their partnership was jeopardised.
Donnelly said: "Financially the other one would get a kickback off that. Every cloud – we have insured each other against that."
McPartlin went on: "The problem with that is that if one of us has a fatal accident, we're the first one that the police will come to because we've got a motive."
The pair famously had a chart career under the guise of PJ and Duncan, a spin-off from their roles in BBC series Byker Grove. But McPartlin said of their songs: "I can't even name them. They're all pretty bad."