Bradley guided a youthful roster to a 4-12 record in his first season at the club, and has made some key signings in the off-season as he looks to further improve his side.
"I'm fortunate enough that I get the chance to be around many head coaches across the NFL," Kelly told reporters. "I have a great relationship with a number of them.
"I think Gus Bradley is one of the finer head coaches that I've been around. I'm a big believer in the way he's built this program. You could see it last year with the way they finished, the buy-in."
Kelly has been head coach of the Fighting Irish since 2010.