Jackson called this pair of hires a "fresh, fresh, fresh 'Idol' one-two!"
Minaj, he said, "brings a whole other cool vibe we've never had on the show, and Keith Urban? My God, he's unbelievably talented!"
When Carey was asked whether she had eagerly awaited news of who would join her as judges, she cracked that, no, she hadn't, "because all I really care about is me," but quickly added, "Only kidding."
Turning serious, she said she didn't know what kind of judge she would be.
"Am I the mean one? Am I the nice one? ... It's not about me, me, me, it's about them (the contestants) and what I can bring to them to help guide them in the right direction," said Carey.
Ryan Seacrest will remain as host when the show returns for its 12th season in January.
"Last night," he said, "we had a chance to really get together for the first time as a group. Everybody made a toast and talked about how special it was that they were here, and why they were here. So we're off to a good start."
Seacrest took note of "the serious and obvious diversity on this panel," adding, "You can see just by the panel the kind of power the show has."
The makeup of the panel has been in flux since Steven Tyler and Jennifer Lopez announced their exits in July. Carey signed on later that month.
"I am thrilled about this year's judges panel," said Mike Darnell, Fox president of Alternative Entertainment. "With an unparalleled star like Mariah, fan-favorite Randy, chart-toppers like Nicki and Keith and our incomparable host Ryan, we've put together one of the most exciting judging panels around."