Edwards attended Sydney Grammar School, which did not offer music at the time. At 15 years of age, Edwards was granted permission to enter the New South Wales Conservatorium of Music to study piano, oboe, harmony, counterpoint and theory during lunch hours and weekends. In 1963, after being awarded a Commonwealth Scholarship to the University of Sydney, he enrolled in a Bachelor of Arts degree, but became frustrated and dropped out after a year. Due to the benevolent intervention of composers Peter Sculthorpe and Peter Maxwell Davies, he was able to earn a scholarship and complete a Bachelor of Music degree at the University of Adelaide's Elder Conservatorium in 1969, where his teachers included Peter Maxwell Davies (then composer-in-residence), Sándor Veress and Richard Meale. During vacations he worked as assistant to Peter Sculthorpe, gaining valuable insight into the working life of a composer. A further Commonwealth Scholarship enabled Edwards to complete his studies with Peter Maxwell Davies in London in 1970, earning a Master of Music degree, after which he spent 18 months composing at a remote Yorkshire farmhouse. Today, Edwards holds higher doctorates from the Universities of Sydney and Adelaide.