Majors played high school football for the Huntland Hornets of Franklin County, Tennessee. They won the state championship in 1951. Majors' father, Shirley Majors, was the head coach at Huntland from 1949 to 1957 and then head coach at The University of the South, Sewanee, from 1957 to 1977. Majors also played alongside his brother, Joe, at Huntland. Another brother, Bobby, also played at Tennessee and professionally for the Cleveland Browns. In all, Majors had four brothers, who all played football. Johnny was the oldest.