Anton was born in Cape Town, South Africa, and started playing the drums at age four. He moved to Boston in the USA when he was 17 and studied both jazz and classical music at the New England Conservatory, graduating in 1975. The following year he moved to New York and began making his name as a freelance musician. He soon met Letterman show MD Paul Shaffer on a session for Joan Armatrading, but it was almost ten years before he got the chance to join Shaffer on the Letterman show.