John Baer was born on July 24, 1919, in Lewiston, Idaho. He attended the University of Idaho from 1937 to 1939, and then entered the U.S. Military Academy at West Point on July 1, 1939, receiving his commission as a 2d Lt in the U.S. Army Air Forces on January 19, 1943. While at West Point, he completed pilot training and was awarded his pilot wings at Spence Field, Georgia, in December 1942. After completing P-47 Thunderbolt training, Applied Tactics training, and Camouflage training, Baer deployed to England and served with the 396th Fighter Squadron of the 368th Fighter Group from December 1943 to June 1945, followed by service as deputy commander of the 368th Fighter Group on occupation duty in Germany from June 1945 to August 1946. During this time, Maj Baer was credited with the destruction of 4 enemy aircraft in aerial combat plus 1 damaged. After returning to the U.S. he served with Headquarters U.S. Air Force from September 1946 to June 1955. His next assignment was as commander of the 67th Tactical Reconnaissance Group at Itami AB, Japan, from August 1955 to August 1956, and then deputy commander of the 35th Fighter Wing at Yokota AB, Japan, from August 1956 to July 1957. Col Baer served on the staff of Headquarters Pacific Air Forces at Hickam AFB, Hawaii, from July 1957 to May 1958, and then returned to Headquarters U.S. Air Force in the Pentagon, from June 1958 to August 1961. He attended National War College from August 1961 to July 1962, and was vice commander of the 48th Tactical Fighter Wing at RAF Lakenheath, England, from July 1962 to July 1963. His next assignment was as commander of the 20th Tactical Fighter Wing at RAF Wethersfield, England, from June 1963 to July 1965. Gen Baer next served on the staff with Headquarters Tactical Air Command at Langley AFB, Virginia, from August 1965 to June 1967, followed by service as deputy commander of U.S. Military Assistance Command Thailand from June 1967 to January 1969. He was director of the Near East and South Asia Region in the Office of the Assistant Secretary of Defense for International Security Affairs at the Pentagon from January 1969 to September 1970, and then served as deputy director for Strike Forces with Headquarters U.S. Air Force in the Pentagon from September 1970 until his retirement from the Air Force on April 1, 1972. Gen Baer was a command pilot and accumulated over 4,000 flying hours during his Air Force Career.

His Silver Star citation reads:

For gallantry in action against the enemy on 23 December 1944. While he was leading a squadron of fighters in the area of Koblenz, Germany, Capt. Baer observed a formation of more than thirty-five FW 190's and ME 109's attacking three boxes of B-26's. Determined to protect the bombers, he directed his squadron in a vigorous assault upon the enemy; and despite their numerical superiority Captain Baer made repeated attacks, and by the force of these assaults nullified the enemy mission. By his unusual aerial proficiency Capt. Baer personally accounted for the destruction of two of the thirteen enemy planes destroyed by his squadron.