The award was presented at the annual ceremony put on by the Charlotte Touchdown Club.
"It means a lot, especially with the journey I have been through," Watts said. "I have played offense, I've played defense and I've kind of bounced around and tried to find a spot to fit on the field my whole career. So this is a tribute to all of the hard work I did and everything coming together."
Watts said his biggest improvement this season was making more game-changing plays.
He has an FBS-leading seven interceptions for the Fighting Irish, along with 47 tackles. He had two picks against both USC and Pittsburgh, becoming the first Irish player to pick off two passes in back-to-back games since 1996.
"Last season I missed out on a few plays and I would be laying in bed just thinking about them all night," Watts said. "So my goal coming into the season was not to make those same mistakes and just come out and ball out. That is pretty much what I've done."
Watts' NFL draft stock has skyrocketed, although he hasn't said if he will enter the draft.
Although he graduated from Notre Dame in May, he still has two years of athletic eligibility remaining because he redshirted in 2020 along with his COVID year exemption.
"Coming into the season I wasn't on anybody's radar because it was my first year starting," Watts said "But things are starting to pick up."
Previous Nagurski award winners include Warren Sapp, Charles Woodson, Champ Bailey, Dan Morgan, Terrell Suggs, Derrick Johnson, Brian Orakpo, Luke Kuechly, Aaron Donald, Bradley Chubb, Josh Allen and Chase Young.