Reber, who was born in Wheaton, Illinois, studied at the Illinois Institute of Technology and became a radio engineer. His work in radio astronomy took him to many places including Washington DC in the late 1940s where he was chief of the Experimental Microwave Research Section, Hawaii, in 1951, and Tasmania in 1954 where he joined the Commonwealth Scientific and Industrial Research Organization. From 1957 to 1961 he worked at the National Radio Astronomy Observatory in Virginia and then returned to Tasmania to complete the studies he had started there.

Reber built the first antenna to be used specifically for extraterrestrial radio observations and was largely responsible for the early developments in radio astronomy. For many years he was probably the world's only radio astronomer. His interest was aroused in 1933 by the work of Karl Jansky. In 1937 he built, in his own backyard, a 30-foot (9.4-m) steerable parabolicbowl-shaped radio reflector with an antenna at its focus. Working at a shorter wavelength than Jansky, 60 centimeters instead of 15 meters, he began to spot emission peaks in the Milky Way. These were the intense radio sources in the constellations Cygnus, Taurus, and Cassiopeia. He published his results from 1940 onward and these came to the attention of many astronomers who, although unable to follow him immediately owing to the war, recognized the value of his work. Over the years Reber constructed several telescopes so that he could map the radio sky at different wavelengths. His Hawaiian instrument operated at 5.5–14 meters while in Tasmania he used radio waves of 144 meters.

It was reading Reber's results that stimulated Jan Oort to pose the problem that led to Hendrik van de Hulst's discovery of the 21-centimeter hydrogen emission.