Born in Sanremo, Obrist studied music in Weimar and in Berlin where he received his doctorate in musicology in 1892.
Afterwards he received a proposition to become Kapellmeister at the Augsburg City Theatre.
From September 1895 to 1900 he was Hofkapellmeister at the Staatstheater Stuttgart (Kingdom of Württemberg), where he made great contributions to the modernization of the repertoire of subscription concerts of the Hofkapelle.
He was married to theatre actress Hildegard Jenicke [de].
Obrist's affair with the opera singer Anna Sutter was to prove fatal.