Brugmans studied at the University of Groningen, where he earned doctorates in medicine and philosophy, and also a masters degree in liberal arts. In 1785 he became a professor of physics and mathematics at the University of Franeker, and in 1786 succeeded David van Royen (1727-1799) as professor of botany at the University of Leiden, where he also became director of Hortus Botanicus Leiden.
In 1795 Brugmans was appointed professor of medicine at Leiden, and also in charge of the Military Medical Service of the newly created Batavian Republic. In 1811 he was appointed inspector-general of the French Imperial Military Health Service. As a military physician, he was instrumental in the establishment of emergency hospital facilities and the improvement of hospital and barrack conditions. Brugmans stressed the importance of sanitary conditions, and fought against the spread of contagious diseases. He is particularly remembered for his expertise regarding gangrene.