Brown is the son of Parker High School football coach Major Brown and his wife, Westfield High School English teacher Eliza Jane Brown. The family moved from the Smithfield Court housing project to 10th Court North on "Dynamite Hill" during his childhood. The neighborhood was targeted by a campaign of racially-motivated bombings that terrorized African American residents. He played woodwinds in the Parker High School band. In 1963 he attended the March on Washington for Jobs and Freedom.
Brown attended Howard University in Washington, D.C., and completed his bachelor of arts in economics at Talladega College in 1965. He married the former Betty Winston and began working at the Jefferson County Committee for Economic Opportunity.
After joining the bar, Brown worked with Civil Rights attorney J. Mason Davis and later became a partner in the firm of Davis & Brown. In 1981 he founded Brown, Chappell & Burrell with Agnes Chappell and Robin Burrell. Chappell left the firm to serve on the Jefferson County Family Court and Burrell moved on in 1989, leaving Brown with a solo practice.
Brown was appointed to the Jefferson County Circuit Court in April 2000 by Governor Don Siegelman to serve out the remaining term of Bill Wynn on the court's criminal division. He transferred to the civil division and was elected to the seat in 2002, 2006 and 2010. In January 2013 he was elected presiding judge, succeeding Scott Vowell.
Brown announced his retirement from the bench in June 2015. Pat Thetford was appointed in October by Governor Robert Bentley to fill his unexpired term. Brown has served as a professional mentor to generations of young lawyers. He has also served on the board of Leadership Birmingham and on the board of trustees of First Congregational Church. In 2019 Brown was one of the activists who founded the Birmingham Committee for Truth and Reconciliation to host an event for Angela Davis at Boutwell Auditorium.
- Faulk, Kent (January 15, 2013) "Jefferson County Circuit Court Judge Houston Brown elected as presiding judge." The Birmingham News
- Faulk, Kent (June 26, 2015) "'You're going to have to shoot me in the back' retiring judge says he once told officer." The Birmingham News
- Burrell, Robin (Spring 2016) "Judge Houston L. Brown." Cumberland Lawyer, pp. 18-21