Glennon was launched on 26 August 1942 by the Federal Shipbuilding & Dry Dock Company, of Kearny, New Jersey, sponsored by Miss Jeanne Lejeune Glennon, granddaughter of Admiral Glennon, and commissioned on 8 October 1942, with Lieutenant Commander Floyd C. Camp in command. Glennon was awarded two battle stars for services in World War II.