Tillerson graduated from Huntsville High School in 1970. He was a section leader for the percussion section of his high school band, in which he played the kettle drums and snare drum, and he earned spots in the all-district and all-region bands during his senior year. Tillerson received a college scholarship from the University of Texas Longhorn Band. He received a bachelor of science degree in civil engineering from the University of Texas at Austin in 1975. During his time at UT Austin, he was involved with the Tejas Club (an all-male secret society) and the marching band.