The former winner will debut the track 'The Last Goodbye', taken from his upcoming second album, on the Thursday night results show, according to The Hollywood Reporter.
"I'm certainly looking forward to meeting the new contestants, and also really excited to meet the new judges," he told the trade publication.
Cook, who triumphed in the seventh season of the Fox competition, previously recorded the farewell song for season ten, a new version of '(Don't You Forget) About Me', originally released by Simple Minds.
He is not the first former American Idol contestant to take to the stage this season. Adam Lambert, Lee DeWyze, Fantasia and Constantine Maroulis have all performed, while Kelly Clarkson will appear on tonight's results show alongside Jason Aldean and Rihanna.
This week saw the Top 8 contestants performing memorable songs from the movies. All contestants' studio performances are now available on iTunes as individual tracks or a compilation album.
American Idol airs Wednesdays and Thursdays on Fox.