A native of Tennessee, Kelso entered the U.S. Naval Academy in 1952 and graduated in the class of 1956. His first service as a commissioned officer was in the attack cargo ship USS Oglethorpe (AKA-100) from 1956 to 1958. During the first half of 1958 he was a student at Submarine School and then served 1958-59 as a junior officer in the diesel submarine USS Sabalo (SS-302). After completing his studies as a student in the Navy's Nuclear Power School he was held over to be an instructor in the school. He then had successive tours in the attack submarine Pollack (SSN-603), as engineer officer of the ballistic missile submarine USS Daniel Webster (SSBN-626), and as executive officer of the attack submarine USS Sculpin (SSN-590). On behalf of Admiral Hyman G. Rickover, he ran the Nuclear Power School, 1968-71. In 1971 Kelso went through a training period in the Nuclear Reactors office prior to commanding his first submarine, the USS Finback (SSN-670), in 1972. In 1972-73 he served on the ComSubLant staff and from 1973 to 1975 commanded the attack submarine USS Bluefish (SSN-676), including a voyage to the North Pole. He served 1975-77 as executive assistant to Admiral Isaac C. Kidd, Jr., CinCLantFlt-CinCLant-SACLant, and commanded Submarine Squadron Seven, 1977-78. In 1978-80 he was submarine detailer in the Bureau of Naval Personnel. From 1980 to 1983 Kelso was assigned to Submarine Directorate, OP-21, in the office of the Chief of Naval Operations. From 1983 to 1985, as a rear admiral, he was director of the Secretary of the Navy's Office of Program Appraisal. In 1985-86, as a vice admiral, he commanded the Sixth Fleet during combat operations in the Mediterranean area. As a four-star admiral, he served as Commander in Chief Atlantic Fleet, 1986-88 and from 1988 to 1990 was double-hatted as Supreme Allied Commander Atlantic and Commander in Chief Atlantic Command. Admiral Kelso was Chief of Naval Operation from 1990 to 1994 and from January to July 1993 was Acting Secretary of the Navy. During his tenure as CNO he presided over the reorganization of the OpNav staff in response to the Goldwater-Nichols Act, directed large-scale reductions in the size of the fleet at the end of the Cold War, provided resource support for the successful U.S. efforts in the 1990-91 Desert Shield/Desert Storm operations against Iraq, and dealt with the effects of the 1991 Tailhook scandal.