Alexandersson attended the Royal College of Music in Stockholm, then studied the violin under Johan Lindberg, counterpoint under Johan Lindegren, and instrumentation under Jean Paul Ertel in Berlin. His musical career had a promising beginning: he received several scholarships, and he was commissioned to write the official march of the Olympic Games in Stockholm 1912. His second symphony, premièred by George Schnéevoigt in 1919, was a success. After writing orchestral music to several Swedish films he devoted more of his time to writing music for silent films, and he played in person, along with, among others, Hilding Rosenberg in the orchestra pit at the Red Mill cinema in Stockholm. He died in poverty in 1927, and the funeral was funded by the City.