Kater was born in Zittau, Germany. He moved to Canada as a teenager where he first studied at St. Michael's college before eventually going onto the University of Toronto where he earned his BA degree in 1959 and then his MA in 1961 respectively. In 1966, while at the University of Heidelberg, he produced a written thesis on the subject of the Nazis' 'Ancestral Heritage' association.
Since 1967, Kater has been teaching at the York University in Toronto. Many of his books have been translated into German.