Stamm was born in Leverkusen, Germany in 1958. At the age of 7, he began study of the piano and pipe organ with Paul Wißkirchen, then organist at the Cathedral of Altenberg. At 11 years old, he began touring Europe as an organ virtuoso and recorded his first track at 13.
Stamm has recorded many works of composers such as Johann Sebastian Bach and Buxtehude. He is renowned for his Bach interpretations and his recording of selected Bach organ works on the famous Trost organ is one of the most popular Bach organ albums to be put to record.