Williams had been suspended by the Tigers after he was charged with a felony in December for allegedly hitting his girlfriend several times and choking her during an argument.
In July, Williams pleaded guilty to peace disturbance, a misdemeanor, and was sentenced to two years of unsupervised probation. He was officially reinstated to the team this week.
Odom told reporters that he is comfortable with how the team handled Williams' situation.
"I've learned you get all the information, you get all the facts, and then you make an informed decision," Odom said. "Through the process of the last eight months or however long it's been, [he] went through with the proceedings in court, and I feel very strongly about how we handled this case and how we've handled every one that we've had since I've been the head coach."
According to the school's student-athlete handbook, Williams would have been permanently barred from playing for Missouri had he been found guilty of a felony charge.
Williams started six games last season as a sophomore. He was suspended for the Tigers' Liberty Bowl appearance following his arrest.
Information from The Associated Press was used in this report.