The son of ESPN analyst Craig James, the James family alleged Adam "had been subjected to actions and treatment not consistent with common sense rules for safety and health" after suffering a concusion during practice.
Leach has denied the allegations, saying that he "would never intentionally harm or endanger a player" and was appealing the suspension when he was informed of the termination.
The Red Raiders will face Michigan State in the Alamo Bowl on Saturday. Defensive coordinator Ruffin McNeill has been appointed to serve as interim head coach.
Leach's record in his 10 years as the Red Raiders' head coach was 84-43.