Edward Randall, Sr., physician and professor, was born on October 7, 1860, in Huntsville, Texas, the son of Samuel and Texana (Garrett) Randall. After his father's death in 1866, Randall's uncle, Edward Randall, a distinguished physician in Galveston, became his mentor. Randall studied at a preparatory school in Lexington, Virginia, and earned a bachelor's degree from Washington and Lee University (1879) and a medical degree from the University of Pennsylvania (1883). After an internship at Philadelphia Hospital, he received postgraduate training in Berlin, Munich, Vienna, and Heidelberg. He returned to Galveston in 1886 and began private practice with his uncle. Randall taught at the reorganized Texas Medical College and Hospital from 1888 to 1891. He then became professor of materia medica and therapeutics at the University of Texas Medical Branch, a position he held until 1928.
He became a dominant figure in the evolution of UTMB. He served as a member of the UTMB executive committee for twenty-five years, a member of the John Sealy Hospital Board of Managers for thirty-nine years (president for thirty-two), a charter member and president of the Sealy and Smith Foundation Board of Trustees for twenty-two years, and a member of the University of Texas Board of Regents for eleven years (1929–40). Randall was especially influential in guiding the development of UTMB's clinical facilities.
He attended many private patients and was viewed by admirers as a true "Southern Gentleman." He was a member and president of the board of directors of the Rosenberg Library, a director of the News Publishing Company and the American National Insurance Company, and a vestryman of Trinity Episcopal Church in Galveston. He was elected president of the Philosophical Society of Texas in 1943. In 1889 Randall married Laura Ballinger; they were the parents of two children, Edward Randall, Jr., and Hallie. Randall died in Galveston on August 12, 1944.