Born in Rodenberg, Hesse (now in Lower Saxony), Köster was active in the Social Democratic Party of Germany (SPD) starting in the early 1880s.
He moved to Groß Ottersleben, near Magdeburg, where he participated in the socialist movement, which was illegal at the time because of the Anti-Socialist Laws, and was a leader in the trade union of the town.
After the sunset of the Anti-Socialist Laws in 1890, he was part of the left-wing opposition known as Die Jungen in the SPD, as the delegate of Wanzleben at the party convention.
Pressured by friends of his, Köster re-joined the SPD and Gustav Landauer and he tried to convince rural workers to join the anarchist movement.
In the same year he became the chief editor of Der Pionier, the theoretical organ of the syndicalist Free Association of German Trade Unions (FVdG), but in 1912, after having spent three months in various prisons, he quit this role and moved to Dresden.