The rock legend died last week at the age of 65 after a battle with cancer.
"Just a few days ago, a true giant was taken from us: Eddie Van Halen," said Clarkson. "He was a legendary guitarist, an amazing musician and an incredible songwriter."
To honor the late icon, the show then aired a clip of Eddie playing with the band Van Halen at the 2015 Billboard Music Awards in Las Vegas -- a rarity as the band did not perform on live television often, according to Clarkson.
The rock group played their hit "Panama" with David Lee Roth providing lead vocals, Eddie's brother Alex on the drums, and Eddie's son Wolfgang playing bass.
"That moment is one that all who saw will always remember," added Clarkson.
Wolfgang joined the band in 2006.
The young Van Halen has shared a handful of throwback photos and videos of his father since he passed.
Most recently, Wolfgang shared a video clip of his dad saying he'd "love to jam with [his] father again."
The video was followed up with a black-and-white photo of Eddie playing music alongside his own father Jan, and a second photo of the rocker on stage with Wolfgang.