Haag was born in Tübingen, Germany. He studied Physics at Technische Hochschule Stuttgart, now the University of Stuttgart, from 1948 to 1954 and then worked on his dissertation in Munich. His supervisor was Fritz Bopp.
From 1956 to 1957 he was at Max Planck Institute in Göttingen. After doing one year each as visiting professor at Princeton University and University of Marseille, he was professor of physics at the University of Illinois at Urbana-Champaign for six years until 1966.
In 1965 he founded the journal Communications in Mathematical Physics, which he guided as Chief Editor for eight years.
He was awarded the Max Planck medal in 1970 and the Henri Poincaré Prize of the International Association of Mathematical Physics in 1997.
It was reported by SZ Gedenken that Haag died on 5 January 2016 at the age of 93.