Jón Ásgeirsson attended the Reykjavík College of Music, studying with Árni Kristjánsson, Dr. Victor Urbancic and Jón Thórarinsson. He continued his education at the Royal Scottish College of Music in Glasgow, and at the Guildhall School of Music in London. In 1996, he was appointed Professor of Music at the College of Education in Iceland.
Since his return to Iceland, Mr. Ásgeirsson has been a productive composer. Among his works are the operas Thrymskvida ( The Lay of Thrym ) and Galdra Loftur, the ballet Blindisleikur (Blindman´s Bluff ), the symphonic poem Lilja, and numerous choral works. The opera Galdra-Loftur, premiéred in 1996 at the Reykjavik Art Festival, is based on a play by Jóhann Sigurjónsson, a passionate tale of a man and his longing for the unknown. In 1995 the Reykjavík Folk Dance Society premiéred Íslenskir söngdansar for choir, orchestra and folk dancers, based on old tunes intended for dancing. Mr. Ásgeirsson has frequently drawn his subject matter from the traditional music heritage of Iceland, particularly evident in his earlier works, such as Folk Songs, Lilja, and Ancient Dances, as well as arranging a number of folk songs for ensembles and choirs.