Edwin S. Cohen grew up in Richmond, Virginia, and at age fifteen entered the University of Richmond, where he took his A.B. in 1933. He then entered law school at the University of Virginia where he served on the editorial board of the Virginia Law Review. He received his law degree in 1936 before his twenty-first birthday. After law school he went to New York and worked from 1936 to 1949 as an associate with Sullivan & Cromwell. There he began to specialize in taxation and investment matters and afterwards gave lectures on the subjects. In 1949 he formed the firm Root, Barrett, Cohen, Knapp and Smith with some of his former law classmates and continued doing tax work for the mutual fund industry. He remained with that practice until 1965.

Cohen had always been interested in teaching, and in 1963, Dean Hardy Dillard offered him the opportunity to teach law at his alma mater, first as a visiting professor and then as a full member of the faculty. In 1968 he was named to the Joseph M. Hartfield Chair. His courses included Tax Practice and Policy, Corporate Income Tax, and Corporate Business and Tax Planning. In 1969 the Nixon administration designated him Assistant Secretary for Tax Policy to work with Secretary of Treasury David M. Kennedy and Under Secretary Charles E. Walker. In 1972 he was appointed Under Secretary of the Treasury and served in that position until his resignation in 1973. After his stint in the Treasury Department Cohen resumed teaching at Virginia and practicing law with Covington & Burling in Washington, D.C. Later he became partner and senior counselor at the firm until his retirement in 1986.

Cohen served on numerous committees, task forces, councils, and clubs throughout his career. From the early 1950s he acted as consultant in various tax matters for the American Law Institute. In 1956 he became part of a seven-member advisory group for the House Ways and Means Committee to consider the revision of the corporate tax rules in the federal tax law. He drafted a revised statute and a report explaining the group's recommendations for corporations, partnerships, estates, trusts and tax administration. In the 1960s he served on a number of federal advisory groups or task forces: in 1965, President's Johnson Task Force to Improve the World-Wide Competitive Effectiveness of American Business; in 1967, the advisory group for the Commissioner of Internal Revenue; and in 1968, the Task Force on Federal Tax Policy to make recommendations to President-elect Nixon. Between 1968 and 1971 he worked with the legislators of Virginia, first as a counselor for the Virginia Income Tax Commission, and later as a member of the Virginia Income Tax Conformity Study Commission. He died in 2006.