Born in Copenhagen, Rosenhoff was a student of Adolph Lund and later of Niels Gade.
When the music academy was established in 1867, Rosenhoff was the acting teacher of piano.
Teaching became Rosenhoff's life's work,[1] and through it he exerted great influence on generations of Danish musicians, including Tekla Griebel-Wandall,[2] Carl Nielsen[3] and Hilda Sehested.
[citation needed] As a composer, he created works of chamber music (quintet, sextet), songs, piano pieces (including pedal studies), and two overtures for orchestra.
He published three collections of exercises for use in music theory lessons.