DeGolyer was born in a sod house on October 9, 1886, the son of John and Narcissa Kagy Huddle DeGolyer of Greensburg, Kansas. He was the eldest of three children. The family moved to Joplin Missouri, where Everette attended school while his father worked in lead and zinc mining in the area. In 1901 the family moved to Norman, Oklahoma, where Everette attended the University of Oklahoma preparatory school. DeGolyer attended the University of Oklahoma beginning in the fall of 1905. During the summers of 1906-1909 he worked for the Unites States Geological Survey, starting as a cook and working up to field assistant. In 1909 DeGolyer began work as a field geologist for the Mexican Eagle Pretolum Company (El Aguila Oil Company), remaining with the company for ten years, where he was involved in the discoveries of the Potrero del Llano No. 4 in 1910 and the Las Naranjas field after 1911. DeGolyer married Nell Virginia Goodrich, a teaching assistant at the University of Oklahoma, in 1910, living in Tampico, Mexico. DeGolyer returned to the University of Oklahoma to finish his A.B. degree in geology, receiving it in 1911.
DeGolyer opened a petroleum geology consultancy in 1914, moving to Montclaire, New Jersey to work in New York City in 1916. In 1919, while working as a consultant to the British entrepreneur Lord Cowdray, DeGolyer negotiated the sale of the El Aguila company to Royal Dutch Shell. In the same year, DeGolyer organized the formation of the Rycade Oil Company as well as the Amerda Petroleum Corporation for Lord Cowdray, rising to become general manager, president, and chairman from 1929 to 1932 DeGolyer left the firm in 1932, but remained with Rycade, which was established to explore salt dome oil deposits through 1941. As a geophysical consultant with Rycade, DeGolyer made the first torsion balance survey in the United States at the Spindletop oilfield. An oilfield found by DeGolyer on behalf of Rycade at Nash, Texas was the first oilfield anywhere to be discovered using geophysics. From 1925 DeGolyer established the Geophysical Research Corporation as a subsidiary of Amerada to develop reflection seismology techniques originated by J. Clarence and Eugene McDermont, leaving in 1932 to move to Dallas, Texas. DeGolyer provided financial support for the 1930 establishment of GRC's successor, Geophysical Service Incorporated GSI went on to spin off Texas Instruments. In 1936 with Lewis MacNaughton, DeGolyer established the petroleum exploration consulting firm DeGolyer and McNaughton, and Core Laboratories, Incorporated the same year to provide drilling core and fluids analysis. DeGolyer was also associated with the Atlatl Royalty Company from 1932 to 1950 and the Felmont Corporation in 1934. In 1956 he established Isotopes, Incorporated to provide radioactive isotopes for oilfield and industrial purposes.
During World War II, DeGolyer served as director of conservation with the Office of The Coordinator for National Defense from 1941 to 1942. He was assistant deputy of the Petroleum Administration for War in 1942-43, and was in charge of the Petroleum Reserves Corporation mission to the Middle East in 1943-44 He was president of the American Institute for Mining and Metallurgical Engineers in 1927, and was a director of the American Petrolum Institue for twenty years. In 1946, working on behalf of the Office of Strategic Services, the forerunner to the Central Intelligence Agency, DeGolyer recruited Jack Crishton of Dallas, to operate a group of companies which frequently were given new names, presumably to make it more difficult to trace their operations. Crichton became a prominent oil and gas industrialist and was the 1964 Republicangubernatorial nominee.