Hampton was born in Galveston, Texas. He attended Ball High School in Galveston, Texas, and was a letterman in football. He was twice named as the District Defensive Player of the Year, and as a senior, he was a Texas Class 5A All-State first-team selection. His Ball High jersey number (No. 63) was retired at a dinner and parade on April 6, 2009. Hampton is the only football player in school history to receive such an honor.
Hampton attended the University of Texas, and started 37 consecutive games for the Texas Longhorns football team between 1997 and 2000. He became the first defensive lineman to lead the team in tackles two consecutive seasons (1999–2000), and recorded 329 tackles (177 solos) to rank 11th on the school's all-time list. Hampton registered 56 quarterback pressures and caused nine fumbles in his college career. He earned consensus first-team All-American recognition as a senior, having received first-team honors from the Football Writers Association of America, The Sporting News, the Walter Camp Foundation. He was also a first-team All-Big 12 Conference selection and the Big 12 Defensive Player of the Year.
Hampton was an All-America first-team selection by the Football Writers Association and Associated Press as a junior in 1999. In 1998 he was named the team's Most Consistent Defensive Player and started every game. That season, he recorded 60 tackles (29 solos) with two sacks and eight stops for losses and registered six quarterback pressures, five pass deflections and recovered one fumble. He also appeared in three games in 1997 before being granted a medical redshirt but played in every game as a true freshman in 1996, starting six at nose guard and recorded 77 tackles (51 solos), one sack and seven stops for losses. In his freshman season he also had three quarterback pressures and a forced fumble. Hampton majored in history.
In 2000, The Daily Texan, the student daily paper at Texas, characterized Hampton as "relentless," even quoting Hampton. "The way I see it, you never know when your last play is going to be," Texas' star defensive tackle said. "So you should go hard all the time. There's no reason to take a play off.." At the time, Hampton was 6'1 and 325 lbs and safety Greg Brown said "I have never seen him take a down off, he's just so intent on destroying people that he never takes time to rest. It's gotta be a gift." Hampton played with Shaun Rogers, a 2nd round pick of the Detroit Lions in 2001 and a Longhorn from 1997–2000; and after Hampton was quoted saying "No one guy can block me. Two guys can probably get it done but never one guy. I can always overpower one," the Daily Texan printed this: "He's says he's never even been caked. Ever," fellow defensive tackle Rogers said. "He says he wasn't even caked in junior high, but I, at least, am humble enough to say that I might have been once or twice. So I'd say some of what he says is questionable."
Hampton was selected in the first round with the 19th overall choice of the 2001 NFL Draft by the Steelers. He quickly emerged as a solid player in the middle of the defensive line while logging considerable time as a rookie. He played in all 48 games through his first three seasons, becoming a highly disruptive force, and winning a trip to the Pro Bowl in 2003. Six games into the 2004 season, he suffered a tear of the anterior cruciate ligament in his right knee and missed the remainder of that year's games.