Salomon was born in Copenhagen. In 1899 he entered the Conservatory in Leipzig and studied there for four years. He also spent some time in Paris studying with Paul Le Flem. From 1903 he worked as an orchestral cellist and violist and appeared as a soloist in Copenhagen, Paris and Stockholm. His greatest success as a composer and conductor was with the opera Leonora Christina which premiered at Det Kongelige Teater in 1926. The opera was successful due to its use of popular style and the performance of the soprano Tenna Frederiksen Kraft in the title role. His output includes two other operas, Duen og slangen (Doves and Serpents; 1925) and Dronning Dagmar (Queen Dagmar; 1928). Among his other works is a lovely Violin Concerto in g, opus 26 from 1916. He died in his native city of Copenhagen.