Wyckoff was born in Geneva, New York, and graduated from Hobart College. He obtained his PhD from Cornell in 1919. Between 1919 and 1938 Wyckoff worked first in the Geophysical Laboratory, New York, and then at the Rockefeller Institute before transferring to the Lederle Laboratories in 1938. He then worked at the University of Michigan (1943–45) and the National Institute of Health (1945–59). He was appointed to the chair of physics and microbiology at the University of Arizona in 1959.

While at the Rockefeller Institute Wyckoff purified various viruses, including that causing equine encephalomyelitis, using an ultracentrifuge. The pure preparations of encephalomyelitis virus were used to develop a killed-virus vaccine which proved effective against the epidemic that was affecting horses in America. This success led to a program for producing typhus vaccine.

In 1944 Wyckoff entered into an unusual and profitable collaboration with the astronomer-turned-biophysicist Robley Williams. Wyckoff was using the electron microscope to photograph viruses but found, as did other virologists of the time, that the amount of information conveyed about the size and shape of the virus was strictly limited.

Wyckoff discussed with Williams the problem of determining the size of a speck of dust that had fallen onto a specimen and been photographed with it. To an astronomer the solution was obvious, for it is a standard procedure to measure the heights of lunar mountains from the length of the shadow cast by them and knowledge of the angle of the incident light source. The problem was to make viruses cast shadows. They placed the specimen in a vacuum together with a heated tungsten filament covered with gold. This vaporized and coated the side of the specimen nearest the filament, leaving a ‘shadow’ on the far side.

This technique of ‘metal shadowing’ opened a new phase in the study of viruses allowing better estimates to be made of their size and shape, as well as revealing details of their structure.