The 38-year-old Odom was defensive coordinator and safeties coach at Memphis the previous three seasons. He'll also coach linebackers at Missouri and will join the team after Steckel coaches in the Citrus Bowl.
The school said in a release Tuesday that contract details were being finalized.
Memphis finished 10-3 and had one of the top defenses in the country.
Odom played linebacker at Missouri from 1996-99 and finished his career ranked fifth with 362 tackles. For nine seasons from 2003-11 he had a variety of roles under coach Gary Pinkel, including three years as safeties coach from 2006-09.