Paula Abdul arrives at the first round of auditions for Fox's "The X Factor.” (Kevin Winter/GETTY IMAGES)

“This show would never have been the same without Paula,” said Cowell, of his show, which has somehow survived without her in Britain, where it originated, and other countries.

“[I] can’t believe I am saying this - I have missed her a lot, and I am thrilled she’s on the show,” Cowell continued.

Cowell and Abdul were teamed up, with Randy Jackson, for several seasons on Fox’s other singing competition series, “American Idol,” but Abdul walked right before the start of season 9 when she could not agree with the network and the producers over a new contract.

More specifically, Abdul was unhappy that she was not being offered the same kind of money that was being offered to “Idol” host Ryan Seacrest and Cowell for their participation.

Since then, Abdul headlined another competition series, this one a dancing show, called “Live to Dance” on CBS that famously flamed out in one season.

"I am excited beyond words to be a part of ‘The X Factor,’” Abdul said in Fox's announcement — and then had a lot more to say.  

MORE: Cheryl Cole officially joins ‘X-Factor’