In 1965 Fröhlich began to study mathematics and physics at Eidgenössischen Technischen Hochschule Zürich. In 1969 he attained under Klaus Hepp and Robert Schrader the Diplom ("Dressing Transformations in Quantum Field Theory"), and 1972 he earned a PhD from the same institution under Klaus Hepp. After postdoctoral visits to the University of Geneva and Harvard University (with Arthur Jaffe), he took an assistant professorship in 1974 in the mathematics department of Princeton University. From 1978 until 1982 he was a professor at Institut des Hautes Études Scientifiques in Bures-sur-Yvette in Paris, and since 1982 he has been a professor for theoretical physics at ETH, where he founded the Center for Theoretical Studies.
Over the course of his career, Fröhlich has worked on quantum field theory (including axiomatic quantum field theory, conformal field theory, and topological quantum field theory), on the precise mathematical treatment of models of statistical mechanics, on theories of phase transition, on the fractional quantum Hall effect, and on non-commutative geometry.
He is best known for introducing rigorous techniques for the analysis of statistical mechanics models, in particular continuous symmetry breaking (infrared bounds)  , and for pioneering the study of topological phases of matter using low-energy effective field theories .
Fröhlich has been married since 1972 and has two daughters.
In 1991 he received with Thomas Spencer the Dannie Heineman prize, in 1997 he received the Marcel Benoist Prize, in 2001 he won the Max Planck Medal of the Deutschen Physikalischen Gesellschaft, and in 2009 he was awarded the Henri Poincaré Prize. He is a member of the Academia Europaea and the Berlin-Brandenburg Academy of Sciences and Humanities. In 2012 he became a fellow of the American Mathematical Society. In 1978, Fröhlich gave an invited address to the International Congress of Mathematicians in Helsinki ("On the mathematics of phase transitions") and in 1994 at the plenary talk of the ICM in Zurich ("The FQHE, Chern-Simons Theory and Integral Lattices"). He also co-authored a book on quantum triviality.