From 1955 to 1960, Noggle taught Latin American history and Western Civilization at New Mexico State University in Las Cruces, New Mexico. In the fall of 1960, he came to LSU, where he focused primarily in the classroom upon historiography and Twentieth Century U.S. history. He taught survey courses, undergraduate classes, honors classes, graduate seminars, and special topics and readings courses. During several summers he taught at his alma mater, Duke, and at Johns Hopkins University in Baltimore, Maryland. Professor Noggle employed not only traditional methods of instruction but works of popular culture and fiction, including John Dos Passos’ U.S.A., film, photography, and popular music, to highlight U.S. history from 1900 to 1950. He added a new course, "The Age of Roosevelt", to the LSU history offerings. He taught the seminar on historiography for 25 years. In his later years, he began to focus on the American West, a subject which had whetted his academic appetite while he lived in New Mexico. Noggle published four books of history:
Teapot Dome: Oil and Politics in the 1920s, a study of the Teapot Dome scandal which tarnished the image of U.S. President Warren G. Harding;
Into the Twenties: The United States from Armistice to Normalcy, a look at the time from the end of World War I into the Harding administration;
The Walter Lynwood Fleming Lectures in Southern History, 1937 – 1990: A Historiographical Essay.
In addition, Noggle penned articles in professional journals and directed the work of more than 75 graduate students. In 1985, LSU designated Noggle as a "Distinguished Alumni Professor" for achievement in teaching. He was a reader of manuscripts submitted to the Louisiana State University Press and served on the Faculty Press Committee. Noggle was affiliated with the Organization of American Historians, the American Historical Association, and the Southern Historical Association. Upon retirement from LSU in 1995, as professor emeritus. Noggle and his wife, Kathleen "Kate" Randall, remained in Baton Rouge. He died there in his library in their home at the age of 89. He had three children, Stephen L. Noggle of Morganton, North Carolina, Vanessa Noggle of Asheville, North Carolina, and Amy N. Ruhin of Atlanta, Georgia, and two grandchildren. A private service and interment was held at Greenoaks Memorial Park in Baton Rouge on Veterans Day 2013. A public memorial service was held on January 19, 2014, at the Lod CookAlumni Center on the LSU campus.
