After graduating from Yakima High School, serving in the United States Navy until the end of World War II, and attending the North Dakota Teachers College, the University of Wisconsin–Madison, and the University of Washington, Corbett remained at Washington to complete his Ph.D. in 1952. He joined the chemistry faculty of Iowa State University and the scientific staff of Ames Laboratory in 1953.  He was affiliated with both institutions for his entire career, and served as chair of the Department of Chemistry between 1968 and 1973. He was elected a Fellow of the American Association for the Advancement of Science. He was awarded two DOE Awards for Outstanding Scientific Accomplishments and Sustained Research in Materials Chemistry, the Humboldt Prize (1985), the 2005 Spedding Award from the Rare Earth Research Conference, the 2008 Monie A. Ferst Award from Sigma Xi, and several ACS Awards for both Inorganic Chemistry and Distinguished Service in the Advancement of Inorganic Chemistry. He was elected to the United States National Academy of Sciences in 1992.