Brown was born Herbert Brovarnik in London, to Ukrainian Jewish immigrants from Zhitomir, Pearl (née Gorinstein) and Charles Brovarnik, a hardware store manager and carpenter. His family moved to Chicago in June 1914, when he was two years old.  Brown attended Crane Junior College in Chicago, where he met Sarah Baylen, whom he would later marry.  The college was under threat of closing, and Brown and Baylen transferred to Wright Junior College.  In 1935 he left Wright Junior College and that autumn entered the University of Chicago, completed two years of studies in three quarters, and earned a B.S. in 1936.  That same year, he became a naturalized United States citizen.  On February 6, 1937, Brown married Baylen, the person he credits with making him interested in hydrides of boron, a topic related to the work in which he, together with Georg Wittig, won the Nobel prize in Chemistry in 1979.  Two years after starting graduate studies, he earned a Ph.D. in 1938, also from the University of Chicago.
Unable to find a position in industry, he decided to accept a postdoctoral position.  This became the beginning of his academic career.  He became an instructor at the University of Chicago in 1939, and held the position for four years before moving to Wayne University in Detroit as an assistant professor.  In 1946, he was promoted to associate professor.  He became a professor of inorganic chemistry at Purdue University in 1947 and joined the Beta Nu chapter of Alpha Chi Sigma there in 1960.  He held the position of Professor Emeritus from 1978 until his death in 2004. The Herbert C. Brown Laboratory of Chemistry was named after him on Purdue University's campus. He was an honorary member of the International Academy of Science, Munich.
During World War II, while working with Hermann Irving Schlesinger, Brown discovered a method for producing sodium borohydride (NaBH), 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. The elements found as initials of his name H, C and B were his working field.
In 1969, he was awarded the National Medal of Science.
Brown was quick to credit his wife Sarah with supporting him and allowing him to focus on creative efforts by handling finances, maintaining the house and yard, etc. According to Brown, after receiving the Nobel prize in Stockholm, he carried the medal and she carried the US$100,000 award.
In 1971, he received the Golden Plate Award of the American Academy of Achievement.
He was inducted into the Alpha Chi Sigma Hall of Fame in 2000.
He died December 19, 2004, at a hospital in Lafayette, Indiana after a heart attack. His wife died May 29, 2005, aged 89.