Dronskowski studied chemistry and physics at the University of Münster from 1981 to 1986. He completed his chemistry diploma with Bernt Krebs and Arndt Simon in 1987. He finished his physics diploma with Ole Krogh Andersen and Johannes Pollmann in 1989. He received his doctorate under supervision of Arndt Simon at the University of Stuttgart. From 1991 to 1992, he was a visiting scientist in the group of Roald Hoffmann at Cornell University. In 1995, he finished his habilitation at the University of Dortmund. Since 1997, he is a full professor at the RWTH Aachen University.