Atanasoff was born in Hamilton, New York, and educated at the universities of Florida, Iowa, and Wisconsin, where he gained his PhD in 1930. He taught at the Iowa State University from 1930 until 1942, when he moved to the Naval Ordnance Laboratory at White Oak, Maryland. After World War II, Atanasoff worked for various technical companies, eventually serving as president of Cybernetics Inc from 1961 until 1982.

The son of a Bulgarian immigrant who was an electrical engineer, Atanasoff was introduced to calculation at the age of nine when his father gave him a slide rule. This was of little use when, in 1930, he was trying to complete his thesis on the electrical properties of helium. Not even a desk calculator could significantly lighten the extensive computations. He began to think about how things could be improved. By 1937 he had opted for a machine that operates digitally, uses capacitors to store binary numbers, and calculates by logic circuits. Working with his assistant, Clifford Berry, Atanasoff built a prototype in 1939 of the suitably named ABC (Atanasoff-Berry Computer). This was good enough to raise sufficient funds to build an operating machine, which was completed in 1942.

Although the ABC was the first device to incorporate a number of key notions, it was unsatisfactory as a working machine. It was slow, could not be programmed, had to be controlled at all times, and suffered from a number of systematic errors. Clearly, it could be improved but the outbreak of war in 1942 took Atanasoff away to other duties. By the time he was free to work on the ABC other workers had seized the initiative. Atanasoff's work long lay forgotten.

This was corrected in a 1973 court case involving two American companies. Sperry Rand had bought the patent to ENIAC and were seeking to charge royalties to other computer manufacturers. Honeywell Inc resisted, claiming that ENIAC was derived from the ABC and from information passed to ENIAC's designer, John Mauchly, by Atanasoff in the early 1940s. Atanasoff gave evidence and the judge found that ENIAC was not the first “automatic electronic digital computer,” and that it was “derived from one Dr. John Vincent Atanasoff.”