Van den Brom started his career at the amateurs of APWC in Amersfoort before signing as a professional footballer for Vitesse in 1986. After seven seasons with Vitesse, playing 225 games and scoring 80 goals, he made the move to Dutch giants Ajax, where he played for two seasons before moving abroad with Turkish side Istanbulspor. He returned to Vitesse after one season, and spent another five seasons there before signing for De Graafschap for his final season, retiring from playing in 2003.
After his playing career he became head scout of De Graafschap and head coach of amateur side Bennekom, before becoming coach of the second team at Ajax, on 29 April 2004. From 2007 to 2010 he served as head coach of small Eerste Divisie club AGOVV Apeldoorn with impressive results, also winning a place in the promotion playoffs in his last season in charge. In May 2010 he was presented as new head coach of Eredivisie club ADO Den Haag, with whom he qualified for the 2011–12 Europa League. In June 2011, Van den Brom was named as head coach of his old club Vitesse. Again, he managed to qualify for the Europa League.
He signed with Belgian side Anderlecht on 29 May 2012 as head coach, but was sacked on 10 March 2014.