Professor Bremer received his doctorate in botany from Stockholm University in 1976, where he worked as lecturer and research assistant in the department from 1972 to 1975, and full-time from 1976.

From 1985 to 1986 he was also a Research Associate and BA Krukoff Curator of African Botany at the Missouri Botanical Garden.

Following this Bremer was installed as Professor of Systematic Botany at Uppsala University in 1989, where he also became head of the department from 1992 to 1999, and Dean of Biology from 1993 to 1999.

In 2006 he received the King's Medal (Hans Majestät Konungens medalj), twelfth level with the Royal Order of the Seraphim (Kungliga Serafimerorden).

The system was published in 1998[6] largely based on the work of Bremer et al. at Uppsala University,[7] and was available on the internet in 1996.