He graduated from Indiana University in 1933 and received a fellowship to work at Lowell Observatory in Flagstaff, Arizona, where he stayed until 1935, working as an observing assistant to Clyde Tombaugh, discoverer of the dwarf planet Pluto.

Nearly 7000 photographic plates for asteroid orbit studies were taken with a 10-inch astrographic camera at the Goethe Link Observatory.

In addition to pursuing studies in stellar kinematics, galactic structure, asteroid astrometry and the history of astronomy, Edmondson served as Program Director for Astronomy of the National Science Foundation (1956–1957), treasurer of the American Astronomical Society (1954–1975) and statistical advisor to Dr. Alfred Kinsey during his studies of human sexuality.

He was also instrumental in creating the Association of Universities for Research in Astronomy (AURA), a consortium of 38 U. S. astronomical institutions and seven foreign affiliates, that manages the three observatories plus the Space Telescope Science Institute which directs research with the Hubble Space Telescope.

He was a member of the Minor Planet Commission of the International Astronomical Union (IAU), and was its president from 1970 to 1973.