Scott was recruited to Hawthorn in the 1994 national draft at pick 60, without playing a game, he was delisted and then re-drafted by Hawthorn in the 1996 draft, where he won the reserves best-and-fairest. Making his senior debut in 1997, Brad played all 22 games and was seen as a very solid contributor, but was traded at the end of that season to the Brisbane Lions, enabling him to play in the same side as his brother Chris.
Scott was a very solid contributor over a number of years with the Lions and was seen as a fearless figure in defence. While defiant, Scott battled numerous injuries including one incurred during his milestone 150th game late in 2005. Like his brother, Scott was renowned for being one of the hardest players in the league. They were both integral members of the Lions' first two premierships in 2001 and 2002. Injuries saw him miss the 2003 premiership and sidelined for the latter part of 2004. Scott's lacklustre form in 2004 and 2005 fed speculation that his contract with the Lions would not be renewed, however he remained with the club and announced on 10 August 2006 that he would retire at the end of the season. Scott played his farewell game in Round 22 against the Saints.
Retirement from playing saw Scott as the development coach at Collingwood, where he had success working closely with a number of young Magpies and other players. Scott was also a candidate for the vacant coaching position at Richmond, however he believed his skill set suited North far better and was appointed as North Melbourne coach for the 2010 season, signing a three-year contract on 17 August 2009. Scott had a terrible start to his coaching career, with three of the first four matches resulting in losses, including a 104-point thrashing from 2009 runners-up St Kilda. Since then, North made steady progress and finished outside the top eight on percentage. Although North Melbourne missed the finals for the second year in succession, Scott was rewarded with a contract extension as Kangaroos coach, with president James Brayshaw stating that he was satisfied with the club's progress under Scott. He led the team to 8th position and a spot in the finals at the end of the 2012 home and away season, with the side winning ten of its last twelve matches since a 115-point loss to Hawthorn in Round 10. The club was then defeated in their elimination final match against West Coast by 96 points. Following North Melbourne's disappointing season in 2013 after losing 10 matches by 16 points or less, the 2014 season began with a positive outlook as Nick Dal Santo was added to North Melbourne's list as a restricted free agent at the end of the 2013 season. With North Melbourne's now silky midfield looking strong, the success of the 2014 season saw Scott lead North Melbourne into his second finals series as coach after finishing 6th at the end of the premiership season. Winning their elimination final match against Essendon by 12 points, then defeating Geelong in the semi final to progress to Scotts' first preliminary final as coach against Sydney, the 71-point loss ended North Melbourne's finals run. The beginning of the 2015 season once again saw Scott make some vital inclusions to North Melbourne's list, with the addition of tall-forward Jarrad Waite and medium forward/midfielder Shaun Higgins. Despite finishing 8th, Scott was under scrutiny after a highly controversial decision to rest 9 players in Round 23 against Richmond, which was deemed by many to be a form of 'tanking'. Scott's 'plan' however, proved to be successful after defeating Richmond in the elimination final the following week by 17 points and going on to defeat Sydney in the semi final to become the first ever team to reach a preliminary final after finishing 8th in the premiership season. North Melbourne's run was ended by West Coast at Domain Stadium by 25 points. Scott currently ranks 3rd for most AFL/VFL games coached without making a grand final and is the only one of those three coaches to do it solely at the one club. Scott resigned as Kangaroos coach on 26 May 2019.
Scott's identical twin brother Chris Scott played alongside him at the Brisbane Lions and is now the coach of Geelong. He is the younger twin by a few minutes. In September 2014, Scott's wife Penny gave birth to their first child, a son.