Henry Eyring was born on February 20, 1901, in the Mormon colony of Colonia Juárez, Chihuahua, México, to Edward Christian Eyring, a wealthy cattle rancher, and Caroline Cottam Eyring (Romney). He called himself a "little Mexican" and a "cowpoke" and remained a Mexican citizen until he became a naturalized United States citizen in 1935.

Because of the revolution against dictator Porfirio Díaz, in 1912, the Eyring family fled to El Paso, Texas, leaving virtually all their possessions behind. In 1914, they moved to Pima, Arizona, where Henry's father bought a farm. Henry attended the Gila Academy at Thatcher, near Pima, and although he worked on the family farm, he earned high grades. In 1919, he entered the University of Arizona at Tucson, from which he received his B.S. degree (1923).

Work in the Inspiration Copper Mining Company of Miami, Arizona, and in the mines of the Butte-Anaconda area...