This is Oregon's fourth straight BCS bowl appearance and fifth overall.
It will be Kansas State's second, and their first since their 2004 Fiesta Bowl appearance.
At one point in the season, it appeared to be a guarantee that the Ducks and Wildcats would meet at season's end, but in Miami for the BCS National Championship.
The Wildcats earned their bid to Arizona by winning their first Big 12 title since 2003, going 11-1 on the season behind the leadership of Heisman Trophy candidate Collin Klein.
For the first time since 2008, the Ducks were not the kings of the west coast, losing the opportunity at a fourth straight conference title after falling to Stanford in overtime on Nov. 17.
Oregon enters the Fiesta Bowl with an at-large bid after Northern Illinois took the only other at-large bid available for the Orange Bowl.
The Ducks are 1-2 in bowl games under Chip Kelly, with a loss and a win in the Rose Bowl and a loss in the 2011 BCS National Championship Game.
It will be the last game for Oregon's Kenjon Barner and the Wildcat's Klein, both of whom are fifth year senior and Heisman hopefuls.
This will be Oregon's return to the Fiesta Bowl, after defeating Colorado 38-16 in the 2002 edition of the game.
Who will win the 2013 Fiesta Bowl?
Kansas State, on the other hand, is winless in their only other BCS Bowl game appearance, falling to Ohio State 35-28 in the 2004 Fiesta Bowl.