Brown was born Herbert Brovarnik in London to Ukrainian Jewish immigrants. He moved to the US at a young age and was educated at the University of Chicago, earning a BS and Ph.D in 1936 and 1938 respectively. He became professor at Purdue University in 1947, a position he still holds.
During World War II, Brown discovered a method for producing sodium borohydride (NaBH4), which can be used to produce boranes, compounds of boron and hydrogen. His work led to the discovery of the first general method for producing asymmetric pure enantiomers.