The son of a Baptist missionary, Williams was born at Nellore in India and educated at the universities of Ottawa, Kansas, and Chicago. He began his career in government service, serving as chemist to the Bureau of Science in Manila before returning to America, where he worked at the Bureau of Chemistry in the agriculture department until 1918. He then moved into industry, working first for Western Electric before joining the Bell Telephone Laboratories in 1924, where he directed the chemistry laboratory until 1945.

With considerable single-mindedness Williams, early in his career, set himself the task of isolating the cause of beriberi. As early as 1896 Christiaan Eijkman had shown that it was a deficiency disease while Casimir Funk had demonstrated that the vitamin whose absence caused the disease was an amine. Beyond that nothing was known when Williams began his work in the Philippines.

Working mainly in his spare time, in 1934 he managed to isolate, from several tons of rice husks, enough of the vitamin, B₁, to work out its formula. In 1937 he succeeded in synthesizing it.

His brother Roger, also a chemist, discovered pantothenic acid, another important vitamin in the B complex.