Born in Chester, South Carolina, Glenn received an Artium Baccalaureus degree from Wofford College in 1912 and a Bachelor of Laws from Oxford University in 1918 before serving as a Captain in the United States Army from 1918 to 1919.

He was in private practice in Chester from 1919 to 1929, serving also as a member of the South Carolina House of Representatives from 1919 to 1923 and as a solicitor and prosecuting attorney for the Sixth South Carolina Circuit from 1923 to 1929.

He was confirmed by the United States Senate on April 29, 1929, and received his commission the same day.

His service terminated on May 2, 1938, due to his death in Chester.

[2] His grandson, Terrell L. Glenn Jr., became an Episcopal priest and an Anglican bishop.