Strömgren was born in 1870 in Helsingborg, in the Scania province of Sweden.
He received his doctorate at Lund University in 1898, becoming docent there the same year.
He worked at the University of Kiel from 1901, and assisted in the publication of Astronomische Nachrichten from 1901 to 1904.
Strömgren worked in a variety of fields but was particularly interested in theoretical astronomy and celestial mechanics, publishing works on the origin and orbits of comets.
He also worked on the calculations for Jens Olsen's World Clock after 1928.