Edgar G. Williams married Joyce, his childhood sweetheart, in 1944. After leaving active duty as a member of the U.S. Army Medical Corps, where he attained the rank of 2nd Lieutenant, he completed his BA in economics and political science in 1947. Afterward, Edgar and Joyce moved to Bloomington, to complete graduate work at Indiana University, where Williams also completed a doctoral degree in business administration, was quickly selected as a faculty member, and soon became a professor of management.

When Williams was appointed chair of the department of personnel and organizational behavior in the School of Business, he began a career in academic administration that would last almost three decades and through six presidents, Wells, Stahr, Sutton, Ryan, Ehrlich, and Brand. Over the years, he published many case studies, articles, and a series of books in his field. Williams served as associate dean of the School of Business, chair of the University Task Force on Management and Organization, executive assistant to the president, vice president for administration, and ultimately as vice president for finance and chief financial officer for the entire Indiana University system. He also served as a consultant to a wide variety of national and international organizations.

After his "retirement" in 1988, he was asked to be the special advisor to the president, interim director of intercollegiate athletics, and interim director of human resources. He also served as president of the Distinguished Alumni Service Association. Williams' many awards include two Sagamores of the Wabash, the IU Presidents Medal, the Thomas Hart Benton Medal, and the Distinguished Alumni Service Medal. Williams had a lifelong interest in sports, and played in varsity basketball, baseball, and football at Evansville. He was also an Honorary I Man, and a member of the IU Athletic Hall of fame.