No one was injured and Hill did not make it past the main office inside the school, police said.
Alexander praised the multiple agencies who worked to end the standoff, saying it could have easily turned into "another Sandy Hook," referring to the elementary school massacre in December 2012.
Suspect's Family Says He Has History of Mental Disorders
While police have declined to comment on a possible motive, the suspect's brother, Timothy Hill, said his brother has a "long history of medical disorders," and it was only a matter of time before he was bound to "do something stupid."
"I honestly can tell you he has got a long history of medical disorders, including bipolar, and that could make you snap on a dime," Timothy Hill told ABC News. "My mom's almost looked like a drugstore at one point. There was so many different medications he was on."
Hill, 22, said he's not close to his brother and believed he last saw him in January 2011. Hill did not disclose his brother's complete mental health history but said he was taking drugs for treating attention-deficit hyperactivity disorder as early as age 6.
Hill said his brother had once threatened to kill him.
"I had a feeling he was going to, eventually, one day, do something stupid, but not of this magnitude," he said.
Natasha Knotts told the Associated Press that Michael Hill lived with her and her husband for a time when he was in his late teens after he started coming to their church.
She said Hill called her sister before the shooting and told her he had a rifle, but did not say what he was planning to do. Knotts said she believed his alleged actions on Tuesday were a cry for help.
"This is something that's totally out of his character. This is not him. This is not the Mike that I know," she said. "For anyone that knew Mike, this was a total devastation."
Police Probing How Suspect Entered School
Authorities believe Hill might have entered the school by closely following a person authorized to enter the building. But once inside, he only went as far as the front office.
"Once we found out where he was located inside the school, we actually gained entry through a side building in the school," DeKalb County Police Det. Clay Hobbs said today on "Good Morning America." "Luckily, we had an officer who was familiar with the layout of the school and made it directly to the office where Antoinette had the man already on the ground, so we could apprehend him and take him into custody."
SWAT teams were sent classroom to classroom to evacuate students, some as young as pre-kindergarten. Authorities have yet to establish a motive or determine whether the suspect had a link to the school.
The shooting came on the second week of classes at the charter school. Classes for the elementary students will be held at McNair High School today.
After her ordeal, Tuff said she would be back to work today.
"Yes, I will be back," she said, "sitting in that same seat, blessing that next person."
ABC News' Mike Levine, Steve Osunsami and Russell Goldman contributed to this report.