Over 13 games this season, Brown recorded 6.5 sacks, 15 tackles for loss and 72 total tackles.
The 6-foot-2, 320-pound junior was a finalist for the Nagurski Trophy, which is given to the nation's top defensive player, and the Outland Trophy, which goes to the nation's best interior lineman.
Brown is considered a potential first- or second-round pick.
"Coach (Chris) Rumph talked to me right after the (Texas Bowl), and I talked to my wife about it," Brown said in a statement. "Then I went and saw Coach (Charlie) Strong yesterday, and we had a good talk about it. I decided to enter the 2015 draft, and that's what everyone thinks is best.
"It wasn't an easy decision because a lot went into it. My wife has school, I have school, and moving the kids around. I got everyone's input on it, but at the end of the day, it's my decision and that's what I came to."
Texas went 6-7 this season.