Hochstrasser was born in Edinburgh, Scotland. In 1952 he received his B.S. from Heriot-Watt University and 3 years later got his Ph.D. from University of Edinburgh. In 1957 he joined the faculty at the University of British Columbia. From 1962 to 1967 he was Alfred P. Sloan Foundation fellow and in 1963 he taught chemistry at University of Pennsylvania. During his 50 years of teaching, he trained 75 Ph.D. students and more than 90 postdoctoral fellows. Between 1955 and 1957 he served in the Royal Air Force. He also published numerous of scientific papers and two books; Behaviour of Electrons in Atoms and Molecular Aspects of Symmetry.
From 1975 to 2012 he was an editor of the scientific journal called Chemical physics. In 1972 he became visiting professor and fellow at Clare College, Cambridge University, England and next year became visiting professor at Australian National University, Canberra. In 1978 he became a Senior Fellow at Alexander von Humboldt Biological Resources Research Institute and the same year became a fellow at American Physical Society. Next year, he became the Director of the University's Regional Laser and Biotechnology Laboratories and in 1980 became visiting professor at University of Munich.