The son of an oil field worker and a school teacher, Sharp grew up in the small farming community of Placedo in Victoria County along the Texas Gulf Coast. In 1972, Sharp earned a Bachelor of Arts degree from Texas A&M University in College Station, where he was a member of the Corps of Cadets and was elected Student Body President. Upon graduation, he was commissioned as a second lieutenant in the United States Army Reserves. He belongs to American Legion Post 76 in Austin.