Kelly has spent the last four years as the head coach at the University of Oregon, leading the college team to victory at the Fiesta Bowl.
Kelly told KEZI-TV: "It's a very difficult decision for me. It took me so long to make it just because the people [at Oregon] are special.
"The challenge obviously is exciting for me, but it's an exciting time and it's a sad time, saying goodbye to people you love and respect, and I wanted to make sure I talked to my players and did it in the right fashion and talked to our staff. I feel I did."