Brown attended Cibolo (TX) Steele in the suburbs of San Antonio, Texas. After running for 2,192 yards and 24 touchdowns as a junior, Brown rushed for 2,596 yards and 30 touchdowns in his senior year, leading Steele to their first-ever Class 5A Division II state championship. He earned a 2010 USA Today High School All-American nomination and played in the 2011 U.S. Army All-American Bowl.
Brown was also a four-year letterman in track & field and played basketball as a freshman. He was a state qualifier as a sophomore and regional qualifier as a junior in the 4 × 200m relay. He also had personal-bests of 11.54 seconds in the 100-meter dash and 22.78 seconds in the 200-meter dash.
Regarded as a five-star recruit by Rivals.com, Brown was listed as the No. 1 running back prospect in the class of 2011. Brown chose the University of Texas over Oklahoma, Florida State, Alabama, Notre Dame, and Stanford.
Brown started the season third on the depth chart behind former running backs Fozzy Whittaker and Cody Johnson. Brown made his first appearance as a Texas Longhorn in the third quarter against the Rice Owls on September 3, 2011. Brown led the longhorns in rushing that game with 86 yards on 16 carries. The next game, against the BYU Cougars, Brown led the Longhorns again with 68 yards on 14 carries and whose 14 yard run on third and 8 sealed the 17-16 win against BYU. On September 17, Brown had his first 100-yard game as he ran for 110 yards on 22 carries and a 16-yard touchdown as he helped the Longhorns defeat the UCLA Bruins 49-20. Brown led the Longhorns in rushing the next 2 games with 63 yards against Iowa State and 54 yards against Oklahoma.
Brown's other breakout performances occurred against Oklahoma State and Kansas. On October 15 he ran for 135 yards on 19 carries and 2 touchdowns in a losing effort to the Cowboys, averaging over 7 yards per carry. On October 29 Brown ran 28 times for 119 yards and 2 touchdowns, helping the Longhorns shutout the Jayhawks, 43-0. However, Brown suffered a foot injury against the Jayhawks and didn't play the next 2 games against Texas Tech and Missouri or the final game of the regular season against the Baylor Bears.
After the injury Brown's performance declined, rushing for only 33, 39, and 35 yards against Kansas State, Texas A&M, and California, respectively. Brown still finished the season as the Longhorns' leading rusher with 742 yards on 172 carries and 5 touchdowns. He was the first true freshman to lead Texas in rushing since Cedric Benson in 2001, and his 74.2 yards per game was second among true freshmen. He was named second team Freshman All-American by Yahoo! Sports.
On May 2, 2015, Brown signed with the St. Louis Rams as an undrafted free agent. He was released by the Rams on September 5, 2015 and was signed to the practice squad the next day. On December 31, 2015, Brown was promoted to the 53-man roster.
On September 10, in the 46–9 victory over the Indianapolis Colts in the season opener, Brown recorded his first career touchdown on a three-yard rush in the fourth quarter.