Brown attended Hermitage High School in Richmond, Virginia, where he played football, basketball and competed in track. He was teammates with Fontel Mines. In basketball, he averaged 15 points and 12 rebounds per game. In track, he competed in the throwing events. He finished 4th in the 2003 Group AAA outdoor shot put competition. He recorded top-throws of 17.32 meters in the shot put and 44.68 meters in the discus throw.
Only 250 lb (110 kg) coming out of high school, Brown was regarded as a three-star tight end prospect by Rivals.com.
Brown attended Virginia Tech, where he played for Frank Beamer's Virginia Tech Hokies football team from 2003 to 2007. After red shirting his freshman year, he played in all 13 games in 2004, and caught his first collegiate pass against Western Michigan Broncos which went for a touchdown. In 2005, he moved from tight end to offensive tackle, where he started every game and played in 673 offensive snaps during the regular season.
As a junior, Brown earned second-team All-Atlantic Coast Conference recognition and was voted state Offensive Lineman/End of the Year by the Richmond Touchdown Club. During his senior season in 2007, Brown switched to left offensive tackle and earned second-team All-ACC honors and Offensive Lineman/End of the Year by the Richmond Touchdown Club for the second consecutive year.
Brown was drafted by the Houston Texans in the first round (26th overall) of the 2008 NFL Draft. He was only the second Virginia Tech offensive lineman ever drafted in the first round of an NFL Draft, after Eugene Chung in 1992. He started all 16 games as a rookie and became the first Texans rookie lineman to start every game since Chester Pitts in 2002. In 2009, Brown protected the blind side of Houston Texans quarterback Matt Schaub who led the NFL with 4,770 passing yards and helped the offense set franchise records with 6,129 total yards and 388 points.
During the 2010 season, he started 12 games, allowing 6.5 sacks and zero holding penalties.
In 2011, Brown was listed on USA Today All-Joe Team and was named second-team All-Pro by the Associated Press, not allowing a single sack or commit a holding penalty.
On August 16, 2012, Brown and the Texans agreed on a six-year, $53.4 million extension, with $22.08 million guaranteed. Brown was in the final year of his rookie contract; the extension will kick in at the conclusion of the 2012 season. Brown was named onto the 2012 All-Pro Team as a first-team selection and was voted to play in the 2013 Pro Bowl at the end of the 2012 season.
On January 3, 2016, Brown tore his quadriceps tendon during the first quarter of a game against the Jacksonville Jaguars. This injury required surgery and Brown was able to return for the 2016 season.
Brown suffered a knee injury during the 2016 offseason and missed the first four games of 2016 before returning in Week 5 and started the final 12 games.
Brown did not attend the Texans' mandatory minicamp as part of a push for a new contract, even though he had two years left on the deal. On July 25, 2017, the Texans placed Brown on the reserve/did not report list after not showing up for the start of training camp.
On November 22, 2011, Brown proposed to Devon Anjelica, a morning show host on Sirius XM's Shade 45. Duane has a daughterand a son.