Rümann was born in Hanover. He studied from 1872 to 1874 at the Academy of Fine Arts, Munich (Akademie der Bildenden Künste München), and from 1880 with Michael Wagmüller. From 1887 he taught at the Academy of Fine Arts, Munich. In 1891, he was raised to the nobility.
Nürnberg, Art Nouveau Silver Medal 1905 by Ruemann, reverse. This large medal was given by the city of Nürnberg to the Royalties attending the ceremony of the unveiling of the monument in honour of Kaiser Wilhelm I on 14 December 1905 in Nuremberg.
Kaiser Wilhelm I Monument (1895), originally in front of the Harmonie Concert and Congress Centre, now in the Alter Friedhof (Old Graveyard) in the Weinsberger Straße
Kaiser Wilhelm I equestrian statue (1905) (designed and begun by Syrius Eberle, who died in 1903; completed by Rümann), Egidienplatz, in front of the Pellerhaus
Statue of Prince Regent Luitpold (1901), station forecourt, removed in 1934, melted down in 1939