Born in Boston, Massachusetts, Woodward was educated at the Massachusetts Institute of Technology, obtaining his PhD in 1937. His whole career was spent at Harvard where, starting as a postdoctoral fellow in 1937, he became Morris Loeb Professor of Chemistry in 1953.

In 1944 Woodward, with William von Eggers Doering, synthesized quinine from the basic elements. This was an historic moment for it was the quinine molecule that William Perkin had first, somewhat prematurely, attempted to synthesize in 1855.

Woodward and his school later succeeded in synthesizing an impressive number of molecules, many of which are important far beyond the field of chemistry. Thus among the most important were cholesterol and cortisone in 1951, strychnine and LSD in 1954, reserpine in 1956, chlorophyll in 1960, a tetracycline antibiotic in 1962, and vitamin B_{1 2} in 1971. The work on the synthesis of B_{1 2} led Woodward and Roald Hoffman to introduce the principle of conservation of orbital symmetry. This major theoretical advance has provided a deep understanding of a wide group of chemical reactions.

He received the Nobel Prize for chemistry in 1965. Woodward's death in 1979 deprived him of a second Nobel award, namely, the chemistry prize awarded to his colleague Hoffmann in 1981 for their work on orbital theory.