Glass was born in Lynchburg, Virginia, and became a newspaper editor. He was elected to the Virginia state Senate in 1899, and was a delegate to the Virginia constitutional convention of 1901-1902. He was one of the most influential members of the convention, which imposed a poll tax and a literacy test in order to disenfranchise African Americans, but which also instituted measures associated with the Progressive movement, such as the establishment of the State Corporation Commission to regulate railroads and other corporations. Glass was elected to Congress as a Democrat in 1902, to fill a vacancy. In 1913, he became Chairman of the House Committee on Banking and Currency, where he worked with Wilson on the Federal Reserve Act. In 1919, Wilson then appointed him Secretary of the Treasury, succeeding William Gibbs McAdoo. His signature as Secretary of the Treasury can be found on series 1914 Federal Reserve Notes, issued while he was in office. He served in that role until 1920, when he was appointed to the United States Senate to fill the vacancy caused by the death of Thomas S. Martin.

Glass served in the U.S. Senate for the remainder of his life, turning down the offer of the Treasury from Franklin Roosevelt in 1933. Glass became Chairman of the Appropriations Committee when the Democrats regained control of the Senate in 1933, and also as President pro tempore from 1941 to 1945. As a Senator, Glass's most notable achievement was passage of the Glass-Steagall Act, which separated the activities of banks and securities brokers and created FDIC insurance. Glass died in Washington, D.C. on May 28, 1946.