Cowell, whose contract ends following the show’s ninth run, said he was offered a lot of money to stay.
“But that wasn’t the reason behind it. I wanted to do something different. I wanted a new challenge,” he said.
It has been reported that Cowell stands to make more money with the X Factor than if he stays on American Idol.
The music industry mogul owns the rights to the X Factor format — and will serve as an executive producer on the US version of the show — meaning he stands to make more than his current reported pay packet of US$36m.
Cowell said there were many people who wanted his Idol job, but said the judges should not be the stars of the show.
“Fundamentally, the most important reason we do this is to find talent,” he said.
Speculation has already begun about who will join Cowell on the X Factor, with former judge Paula Abdul, who left American Idol last year, among the leading contenders.
“I adore Paula. Whatever happens, I will be working with her in some capacity, because I miss her,” Cowell said.
However, he did rule out former Spice Girl Victoria Beckham — who briefly joined the judging panel on American Idol last year.
The star said he wanted to leave the show “on a high” and added he was “very proud of what the show has achieved”.
In a statement released by Fox, Cowell said: “I’m thrilled that we have put a date on the launch of the US version of The X Factor, and delighted to be continuing to work with Fox.
“We have a fantastic relationship, a great team and are all very excited about this.”
Peter Rice, chairman of entertainment for Fox, refused to discuss a possible replacement judge for Cowell on American Idol.
“We have to take our time on that,” he said.
“We have to make sure the chemistry of the judges is as good as it can be.”
American Idol has been the country’s most popular television programme for the last five years and has launched stars such as Kelly Clarkson, Carrie Underwood and Chris Daughtry.
However, viewing figures have been shrinking since its 2005 peak when it averaged more than 30 million weekly viewers.
In April last year, the show attracted 22,3 million viewers. — BBCOnline.