The video was obtained by TMZ Sports and shows a verbal dispute between the two starting cornerbacks.
In the video, Austin steps toward Durham, who pushes back at him. Durham then assumes a boxing posture and unleashes a single punch to Austin's jaw, sending him to the ground unconscious. Durham then comes over and tries to pick up his teammate when the video ends.
"The incident occurred during the spring, which gave Lance and me an opportunity to discuss the matter and put it aside a long time ago," Durham said in a statement released Tuesday night. "Lance and I have always had a brother-like relationship and brothers sometimes fight but, as I said before, the situation should have been handled in a more mature manner."
TMZ reports the altercation took place at Georgia Tech's athletic facility.
"Georgia Tech's football coaching staff became aware of the incident between teammates and friends shortly after it occurred. Discipline was handled internally," the school said in a statement.
Austin and Durham have played in all of the Yellow Jackets' games this season.
"Step Durham apologized and we long ago put that incident behind us," Austin said in a statement. "As far as I'm concerned, there's no further need for an apology. I forgave him already and we have since played well together as teammates this season. Like Step said, as brothers, we have put our aside our differences and our friendship remains strong."
ESPN's Andrea Adelson contributed to this report.