Wallace was born at Colbeck Street, Waterford, Ireland. Both of his parents were Irish; his father, Spencer Wallace of County Mayo, one of four children, who was born in Killala, County Mayo in 1789, became a regimental bandmaster with the North Mayo Militia based in Ballina. William was born while the regiment was stationed for one year in Waterford, one of several successive postings in Ireland and the UK. The family returned to Ballina some four years later, in 1816, and William spent his formative years there, taking an active part in his father's band and already composing pieces by the age of nine for the band recitals.