In 1878 he traveled to Paris, where he studied cello with Auguste Franchomme and music theory with Augustin Savard. He also studied with Jules Massenet at the Conservatoire de Paris.
One of five children, each with an artistic bent, his talent was encouraged from youth. By the time of his return to Norway, in 1884, he had already written a number of works. Schjelderup was introduced to the work of Richard Wagner while in Paris, and went to Germany for further exposure to his work.
This in turn inspired him to write operas, which were to prove the bulk of his output, though he also composed a number of orchestral and chamber works.
He also wrote on music for Norwegian publications, and wrote biographies of Edvard Grieg and of Wagner. In 1921 he published the first Norwegian history of music
Schjelderup was among the founders of the Norwegian Society of Composers in 1917, and from that year until 1920 served as its chairman. He continued to promote Norwegian music despite living abroad.
He died in Benediktbeuern, Bavaria, Germany, in 1933.
Letters by Gerhard Schjelderup held by the State Archives in Leipzig, company archives of the Music Publishing House C.F.Peters (Leipzig).