He studied with Edward Dent at Trinity College, Cambridge, and with Charles Wood and Ralph Vaughan Williams at the Royal College of Music, where he himself taught composition and music theory from 1921 to 1939. From 1937 to 1952, he also served as the Vice President of the British Federation of Music Festivals.

Amstrong Gibbs composed one opera, one operetta, incidental music for several plays, several cantatas, three symphonies, a concertino for piano and string orchestra, five string quartets, one violin sonata, pieces for piano, works for choir, and many songs, a great number of which were settings of texts penned by his friend Walter de la Mare.