Clarkson beat Justin Guarini to win the first season of American Idol in 2002, which featured Cowell, Abdul and Jackson as judges. The trio praised Clarkson as a "game changer" for the show.
"I actually genuinely do not believe we would be sitting here today if you had not entered the show," Cowell told Clarkson. "When you delivered that moment on that first live show and when you sang that winning song at the end..."
"It was a game changer," Abdul said.
Abdul, Cowell and Jackson served as judges for 9, 10 and 13 seasons, respectively. Cowell expressed his desire to make a show with Abdul and Jackson in the future.
"If I had one wish, it would be to make another show with us again," Cowell told Abdul and Jackson.
"Apart from the fact that we had so much fun, to credit you, Kelly, we wouldn't be here without you," he added. "Our legacy, genuinely, are the artists, starting with [Clarkson], who we discovered over a seven-year period. That's what I'm most proud of."
Clarkson released her debut studio album, Thankful, in 2003 following her American Idol win. She released her eighth album, Meaning of Life, in October 2017, and the single "Broken & Beautiful" for the UglyDolls soundtrack in March.