Born in Brooklyn, New York, on February 12, 1899. He graduated from Stevens Institute of Technology in 1919 with a mechanical engineering degree.
Upon graduation, McDermott began working for the Goodyear Rubber Company. In 1923, he began employment with Western Electric Company where he first met J. Clarence Karcher. This experience inspired in McDermott a desire for graduate studies. Earlier Everette Lee DeGolyer, vice president and general manager of Amerada Petroleum Corporation of Dallas, had learned of Karcher's 1921 experiments with the seismograph and held a meeting with Karcher that resulted in the creation of Geophysical Research Corporation (GRC) of Tulsa where Karcher was made vice president. This was as a subsidiary of Amerada. McDermott received a Master of Arts in physics from Columbia University in 1925 and immediately began to work for his friend Karcher. GRC introduced the seismic reflection method which was quickly accepted by the petroleum industry as a promising new tool during the next five years.
In 1930, with the backing of DeGolyer, now president of Amerada, Karcher and McDermott launched Geophysical Service, a pioneering provider of seismic exploration services to the petroleum industry with Karcher serving as president and McDermott as vice-president. McDermott's early work in petroleum exploration led to multiple papers and five patents. During the first year of operation McDermott hired Cecil H. Green. These two would have a lasting relationship for the next 43 years. In 1939 the company reorganized as Coronado Corp., an oil company with Geophysical Service Inc (GSI), now as a subsidiary. On December 6, 1941, McDermott along with three other GSI employees, J. Erik Jonsson, Cecil H. Green, and H.B. Peacock purchased GSI, During World War II, GSI built electronics for the United States Army Signal Corps and the Navy. After the war GSI continued to produce electronics. The rugged nature of equipment for the oil industry and of military equipment were similar and thus continued expansion into military contracts was a natural progression. In November 1945 Patrick E. Haggerty joined GSI.
In 1951, McDermott, along with Cecil Howard Green, Patrick E. Haggerty, and J. Erik Jonsson co-founded Texas Instruments. This was done when the company changed its name to Texas Instruments; GSI becoming a wholly owned subsidiary of the new company. This acknowledged that the company had changed it focus from one primarily devoted to oil exploration to one focused on manufacturing. McDermott was the Chairman of TI from 1951-1957, was Chairman of the Executive Committee of Board of Directors from 1957-1964 and was a Director until his death in 1973. During this period of time, Texas Instruments rose to be one of the world's largest corporations.
A scientist and businessman, McDermott was particularly interested in improving education, which he called "biological humanics." Along with Cecil Green, he was a co-founder of St. Mark's School of Texas in 1950; their endowment included the donation of a planetarium, observatory, and math-science quadrangle. He was also a major donor to many universities and served on the boards of Southern Methodist University, Massachusetts Institute of Technology (MIT), and Southwestern Medical School in Dallas. He also co-founded the Graduate Research Center of the Southwest in 1961, which became the University of Texas at Dallas (UTD) in 1969. In 2001, his wife Margaret endowed the Eugene McDermott Scholars Program at UTD.
The couple also gifted Fredericksburg, Texas with a home for the county's Pioneer Memorial Library by restoring the 1882 Gillespie County Courthouse.
McDermott was actively involved in the arts, serving not only on the Boards of the Dallas Public Library, the Dallas Museum of Art, and the Dallas Symphony Orchestra, but also helping conceive of the Margo Jones Theatre, an early experiment in theatre in the round.
The annual Eugene McDermott Award in the Arts was created at MIT in 1974, and carries a $100,000 stipend as of 2014. The Award celebrates individuals whose artistic trajectory reveals that they will achieve the highest distinction in their fields and continue to produce inspiring work for many years to come. The stipend represents an investment in the recipient’s future creative work, rather than a prize for a particular project or lifetime of achievement. The awardee becomes an artist in residence at MIT, studying and teaching for a period of time.