Smith was born in Williamson County, Texas in a family with 13 children. his parents were tenant farmers. He graduated from Texas Tech University. He owned several movie theaters by the mid 1940s. He was elected to the Texas House of Representatives in 1944 and to the Texas Senate in 1956. He was elected lieutenant governor in 1962. He was elected governor of Texas in 1968 and served from 1969 to 1973.