Born and raised in the village of Tielen (in the Kempen region, just on the Belgian side of the Belgian-Dutch border), he was the youngest child in a family of eleven. When sixteen years old, he began his studies at the Lemmens Institute in Mechelen (since moved to Leuven), which was named after the nineteenth-century organist Jacques-Nicolas Lemmens. At this college, his teachers were Lodewijk Mortelmans, Jules Van Nuffel and Oscar Depuydt. Depuydt was well known at the time for his collaboration with the Desmet brothers on the first set of Gregorian accompaniments produced by the Lemmens Institute.
Peeters would later collaborate with Nuffel and the Institute's other professors, to produce the Nova Organi Harmonia. In 1923 he became an organ teacher at the Institute; simultaneously he acquired the position of chief organist at the St. Rumbold's Cathedral in Mechelen, which he held for most of the rest of his life; Nuffel had already been choirmaster there for many years.
As an organist and pedagogue, Peeters enjoyed great renown, giving concerts and liturgical masterclasses all over the world. He also made recordings of sixteenth-, seventeenth- and eighteenth-century organ music; some of these have been reissued in recent years on compact disc. Most of his own pieces (he wrote well over 100) were for his own instrument, for choir, or for both.