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Morgan, who was born in Bethesda, Tennessee, studied at the Washington and Lee University and then at the University of Chicago where he obtained his BSc in 1927 and his PhD in 1931. The following year, he took up an appointment at the Yerkes Observatory, where he served as professor from 1947 to 1966 and Sunny Distinguished Professor of Astronomy from 1966 to 1974. He was Director of the Yerkes and McDonald observatories from 1960 to 1963.

The standard system of spectral classification of stars, the Henry Draper system, assigned the majority of stars to one of the classes, O, B, A, F, G, K, or M, which were each subdivided into ten categories numbered from 0 to 9. In this classification our Sun is assigned the number G2. Useful as the Draper system is, Morgan realized that it had its limitations. He pointed out that the system was based only on the surface temperature of stars and commonly produced cases where two stars, like Procyon in Canis Minor and Mirfak in Perseus, fell into the same spectral class, F5 in this case, yet differed in luminosity by a factor of several hundreds.

Consequently, in collaboration with Philip Childs Keenan and Edith Kellman, he introduced the Yerkes system or MKK system(also known as the Morgan–Keenan classification) in 1943 in An Atlas of Stellar Spectra with an Outline of Spectral Classification. The new system was two dimensional, containing in addition to the spectral typing a luminosity index. This was used to classify stars in terms of their intrinsic brightness by means of Roman numerals from I to VI, and ranged from supergiants (I), giants (II and III), subgiants (IV), main-sequence stars (V), to subdwarfs (VI). Procyon thus becomes a F5–sp;IV star while Mirfak is a distinguishable F5–sp;I supergiant.

In the 1940s Walter Baade had shown that hot O and B stars were characteristic members of the spiral arms of a galaxy. Morgan and his colleagues thus began to trace out the structure of our own Galaxy by searching for clouds of hydrogen ionized by O and B stars. By 1953 they claimed to have identified the Perseus, Orion, and Sagittarius arms of the Galaxy, thus providing good evidence for its spiral structure. Morgan also worked on star brightness and discovered so-called ‘flash’ variables – stars that change their luminosity very quickly.