Johnson was injured in September 2009 when a barbell fell on his throat. His throat and larynx were almost completely crushed by the bar.
He remained hospitalized for two weeks.
The bench press barbell was loaded with 275 pounds. An assistant strength and conditioning coach was acting as a spotter, according to the LA Times.
After several surgeries, he was signed by the Tennessee Titans.
In a statement, school officials said the university was not at fault, and they are disappointed that Johnson filed the lawsuit.