Born Sidney Clay Judson at Lexington, Kentucky, on February 6, 1892 to Alice Clay Judson and General William Voorhees Judson, Clay Judson earned his A.B. at Harvard and his law degree at University of Chicago. In 1917, he enlisted in the United States Army and served as a captain during World War I. He served in France and Germany for 17 months during 1918-1919, but saw very little combat. Instead, he took a law course at the Faculté de Droit at the Université de Paris. Following his return to Chicago, he taught at the University of Chicago and then worked at several law firms.

In 1921, Judson married Sylvia Shaw, a sculptor and the daughter of a prominent Chicago family. They had two children: Alice, born in 1922, and Clay, Jr. born 1924.

Judson served as a trustee or officer in many charitable and educational organizations, including the Francis W. Parker School, the Chicago Zoological Society, and the Chicago Council on Foreign Relations, among others. Prior to World War II, he was on the Executive Committee of the America First Committee, an organization dedicated to keeping the United States out of the war. During World War II, he was a member of the Price Adjustment Board of the Chicago Ordinance District.

Judson died on November 29, 1960.