Odom played at Missouri and has coached there since 2003, working mostly in operations. He was elevated to safeties coach in 2009.
Odom will remain with Missouri through its bowl game.
He inherits a defense that allowed 35.1 points per game, which ranked 106th in the nation. The Tigers were, however, in the Top 10 of turnovers forced.
Odom is the latest in a string of hires that Fuente has made since last Thursday. He has filled most positions on the coaching staff but has yet to make a decision on his offensive coordinator.