Woodward was born in Boston, Massachusetts, to Margaret (née Burns, an immigrant from Scotland) and Arthur Chester Woodward, son of Roxbury, Massachusetts apothecary, Harlow Elliot Woodward. When Robert was one year old, his Father died in the flu pandemic of 1918.

From a very early age, Woodward was attracted to and engaged in private study of chemistry while he attended a public primary school, and then Quincy High School, in Quincy, Massachusetts. By the time he entered high school, he had already managed to perform most of the experiments in Ludwig Gattermann's then widely used textbook of experimental organic chemistry. In 1928, Woodward contacted the Consul-General of the German consulate in Boston (Baron von Tippelskirch ), and through him, managed to obtain copies of a few original papers published in German journals. Later, in his Cope lecture, he recalled how he had been fascinated when, among these papers, he chanced upon Diels and Alder's original communication about the Diels–Alder reaction. Throughout his career, Woodward was to repeatedly and powerfully use and investigate this reaction, both in theoretical and experimental ways. In 1933, he entered the Massachusetts Institute of Technology (MIT), but neglected his formal studies badly enough to be excluded at the end of the 1934 fall term. MIT readmitted him in the 1935 fall term, and by 1936 he had received the Bachelor of Science degree. Only one year later, MIT awarded him the doctorate, when his classmates were still graduating with their bachelor's degrees. Woodward's doctoral work involved investigations related to the synthesis of the female sex hormone estrone. MIT required that graduate students have research advisors. Woodward's advisors were James Flack Norris and Avery Adrian Morton, although it is not clear whether he actually took any of their advice. After a short postdoctoral stint at the University of Illinois, he took a Junior Fellowship at Harvard University from 1937 to 1938, and remained at Harvard in various capacities for the rest of his life. In the 1960s, Woodward was named Donner Professor of Science, a title that freed him from teaching formal courses so that he could devote his entire time to research.

Culminating in the 1930s, the British chemists Christopher Ingold and Robert Robinson among others had investigated the mechanisms of organic reactions, and had come up with empirical rules which could predict reactivity of organic molecules. Woodward was perhaps the first synthetic organic Chemist who used these ideas as a predictive framework in synthesis. Woodward's style was the inspiration for the work of hundreds of successive synthetic chemists who synthesized medicinally important and structurally complex natural products.

In 1938 he married Irja Pullman; they had two daughters: Siiri Anna (b. 1939) and Jean Kirsten (b. 1944). In 1946, he married Eudoxia Muller, an Artist and technician whom he met at the Polaroid Corp. This marriage, which lasted until 1972, produced a daughter, and a son: Crystal Elisabeth (b. 1947), and Eric Richard Arthur (b. 1953).

During the late 1940s, Woodward synthesized many complex natural products including quinine, cholesterol, cortisone, strychnine, lysergic acid, reserpine, chlorophyll, cephalosporin, and colchicine. With these, Woodward opened up a new era of synthesis, sometimes called the 'Woodwardian era' in which he showed that natural products could be synthesized by careful applications of the principles of physical organic chemistry, and by meticulous planning.

In 1944, with his post doctoral researcher, william von Eggers Doering, Woodward reported the synthesis of the alkaloid quinine, used to treat malaria. Although the synthesis was publicized as a breakthrough in procuring the hard to get medicinal compound from Japanese occupied southeast Asia, in reality it was too long and tedious to adopt on a practical scale. Nevertheless, it was a landmark for chemical synthesis. Woodward's particular insight in this synthesis was to realise that the German Chemist Paul Rabe had converted a precursor of quinine called quinotoxine to quinine in 1905. Hence, a synthesis of quinotoxine (which Woodward actually synthesized) would establish a route to synthesizing quinine. When Woodward accomplished this feat, organic synthesis was still largely a matter of trial and error, and nobody thought that such complex structures could actually be constructed. Woodward showed that organic synthesis could be made into a rational science, and that synthesis could be aided by well-established principles of reactivity and structure. This synthesis was the first one in a series of exceedingly complicated and elegant syntheses that he would undertake.

In the early 1950s, Woodward, along with the British Chemist Geoffrey Wilkinson, then at Harvard, postulated a novel structure for ferrocene, a compound consisting of a combination of an organic molecule with iron. This marked the beginning of the field of transition metal organometallic chemistry which grew into an industrially very significant field. Wilkinson won the Nobel Prize for this work in 1973, along with Ernst Otto Fischer. Some historians think that Woodward should have shared this prize along with Wilkinson. Remarkably, Woodward himself thought so, and voiced his thoughts in a letter sent to the Nobel Committee.

For his work, Woodward received many awards, honors and honorary doctorates, including election to the National Academy of Sciences in 1953, and membership in academies around the world. He was also a consultant to many companies such as Polaroid, Pfizer, and Merck. Other awards include:

In the early 1960s, Woodward began work on what was the most complex natural product synthesized to date—vitamin B₁₂. In a remarkable collaboration with his colleague Albert Eschenmoser in Zurich, a team of almost one hundred students and postdoctoral workers worked for many years on the synthesis of this molecule. The work was finally published in 1973, and it marked a landmark in the history of organic chemistry. The synthesis included almost a hundred steps, and involved the characteristic rigorous planning and analyses that had always characterised Woodward's work. This work, more than any other, convinced organic chemists that the synthesis of any complex substance was possible, given enough time and planning (see also palytoxin, synthesized by the research group of Yoshito Kishi, one of Woodward's postdoctoral students). As of 2016, no other total synthesis of Vitamin B₁₂ has been published.

While at Harvard, Woodward took on the directorship of the Woodward Research Institute, based at Basel, Switzerland, in 1963. He also became a trustee of his alma mater, MIT, from 1966 to 1971, and of the Weizmann Institute of Science in Israel.

Woodward won the Nobel Prize in 1965 for his synthesis of complex organic molecules. He had been nominated a total of 111 times from 1946 to 1965. In his Nobel lecture, he described the total synthesis of the antibiotic cephalosporin, and claimed that he had pushed the synthesis schedule so that it would be completed around the time of the Nobel ceremony.

His lectures frequently lasted for three or four hours. His longest known lecture defined the unit of time known as the "Woodward", after which his other lectures were deemed to be so many "milli-Woodwards" long. In many of these, he eschewed the use of slides and drew structures by using multicolored chalk. Typically, to begin a lecture, Woodward would arrive and lay out two large white handkerchiefs on the countertop. Upon one would be four or five colors of chalk (new pieces), neatly sorted by color, in a long row. Upon the other handkerchief would be placed an equally impressive row of cigarettes. The previous cigarette would be used to light the next one. His Thursday seminars at Harvard often lasted well into the night. He had a fixation with blue, and many of his suits, his car, and even his parking space were coloured in blue. In one of his laboratories, his students hung a large black and white photograph of the master from the ceiling, complete with a large blue "tie" appended. There it hung for some years (early 1970s), until scorched in a minor laboratory fire. He detested exercise, could get along with only a few hours of sleep every night, was a heavy smoker, and enjoyed Scotch whisky and martinis.

That same year, based on observations that Woodward had made during the B₁₂ synthesis, he and Roald Hoffmann devised rules (now called the Woodward–Hoffmann rules) for elucidating the stereochemistry of the products of organic reactions. Woodward formulated his ideas (which were based on the symmetry properties of molecular orbitals) based on his experiences as a synthetic organic chemist; he asked Hoffman to perform theoretical calculations to verify these ideas, which were done using Hoffmann's Extended Hückel method. The predictions of these rules, called the "Woodward–Hoffmann rules" were verified by many experiments. Hoffmann shared the 1981 Nobel Prize for this work along with Kenichi Fukui, a Japanese Chemist who had done similar work using a different approach; Woodward had died in 1979 and Nobel Prizes are not awarded posthumously.