Argelander was born in Memel in the Kingdom of Prussia (now Klaipėda in Lithuania), the son of a father of Finnish descent, Johann Gottlieb Argelander, and German (Prussian) mother, Dorothea Wilhelmina Grünlingen. He studied with Friedrich Bessel, and obtained his Ph.D. in 1822 at University of Königsberg. From 1823 until 1837, Argelander was the head of the Finnish observatory, first in Turku and then in Helsinki. He then moved to Bonn, Germany. There he designed and built a new observatory at the University of Bonn with funding approved directly by King Frederick William IV whom Argelander had become friends with in his childhood. (This lifelong friendship started when the then crown prince temporarily lived in Argelander's parents house after the Prussian royal family fled to Memel after the Battle of Jena–Auerstedt during the Napoleonic Wars.)