Robert Cook Edwards was born 25 March 1914 in Fountain Inn, South Carolina, the son of John T. and Effie Cook Edwards. Edwards entered Clemson College as a freshman at age 15 and graduated in 1933 with a Bachelor of Science degree in textile engineering. His career in textile management began as supervisor of the quality control laboratory of the Dunean Mill, a division of J. P. Stevens and Company, in Greenville, South Carolina. Later he worked as plant manager for the Charles B. Thoms Company, Red Springs, North Carolina, and as plant superintendent at Aberfoyle, Inc., Norfolk, Virginia. Although Edwards interrupted his career in textiles to enter active service in the United States Army in 1942 (Edwards rose to the rank of major), he resumed his work in textiles in 1946, first as treasurer and then as general manager of the Abbeville Group of Deering-Milliken Mills.

In 1956 Edwards returned to Clemson College as Vice-President for Development. At once, he became an active participant in the legal struggle with the Army Corps of Engineers concerning the inundation of Clemson College lands brought on by the construction of Hartwell Dam. The outcome of the litigation resulted in the recovery of several hundred acres of Clemson land. In 1958, on the death of President Poole, the Board of Trustees named Edwards Acting President, and in April 1959 the Board elected him President. Under Edwards' twenty-one year administration, Clemson College changed dramatically: University status was acquired, African-Americans and women were admitted, and six colleges were established. Approximately $78 million was spent on permanent improvements.

Edwards, who retired in 1979, has served on the boards of directors of several corporations such as Duke Power and Dan River, and in leadership capacities in numerous educational organizations. He and his wife, Louise Odum Edwards, had two children, Nancy Louise and Robert C. Edwards, Jr.