Brown grew up in Trenton, New Jersey until age six, when his family relocated to his grandmother's ten-acre farm in rural Chesterfield Township, New Jersey following the death of his grandfather. His father Albert operated a septic tank service and raced at the sportsman level. Brown maintained the family cars as a child and began racing motorcycles at age six, adding motocross at twelve on a course he built himself on the farm.
An exceptional track and field athlete, Brown attended Northern Burlington County Regional High School and went on to Mercer County Community College in New Jersey, where he graduated in 1997 with an associate's degree in business administration. He was fast enough in the 100-meter dash to qualify for the U.S. Olympic Trials that year. He was subsequently offered a full scholarship to run track for Long Island University, but a contact from NFL player Troy Vincent — married to Brown's cousin — redirected him toward professional drag racing.
Brown began competing in the NHRA's Pro Stock Motorcycle division in 1998, spending his first three years with Vincent's Team 23 Racing. He remained in the class through 2007, accumulating 16 wins and recording a best championship finish of second in points, in 2001 and again in 2006. The motorcycle division gave him a thorough foundation in NHRA competition before his move to the premier Top Fuel category.
In 2008, Brown transitioned to Top Fuel dragsters, making him one of the few drivers to have competed at the highest level in two distinct NHRA disciplines. He won his first Top Fuel world championship in 2012, becoming the first African American to claim a national motorsport title in any sanctioning body.
He added two back-to-back championships in 2015 and 2016, and a fourth title in 2024, cementing his standing as one of the most decorated drivers in modern Top Fuel history. His 80 career NHRA wins across both motorcycle and Top Fuel categories place him among the sport's elite performers.
Brown currently competes under his own AB Motorsports banner, driving the Matco Tools Top Fuel dragster.
Brown resides in Pittsboro, Indiana with his wife Billie Jo and their three children, Anson, Adler, and Arianna. He has spoken publicly about his Christian faith.
Beyond racing, Brown has maintained a media presence: he appeared as an appraiser on the A&E reality programme Storage Wars and served as a drag racing instructor for Idris Elba in the television series Idris Elba: No Limits. He has also co-hosted Top Gear America with Tom Ford and William Fichtner.