Born in Hamburg, he studied at the Conservatory of his hometown and later settled down in Wandsbek as director of choral societies, being appointed in 1897 as a teacher of Matthias-Claudius-Gymnasium.
After confirmation in 1873, he left school and, on the advice of his teacher Scheibler, began training for the teaching profession.
At the age of 15, he got a job as a preparatory at the Protestant church school in the neighbouring town of Hamm.
Rüter lived in Hamburg-Hamm on the 2nd floor of the house at Kampstraße 84, which was renamed "Rüterstraße" in his honor in 1951.
A significant portion of Rüter's work was destroyed on 30 July 1943 in the Bombing of Hamburg in World War II, including his first, fourth, fifth, sixth, and seventh symphonies.