Johnson was born near Stonewall, Texas, on August 27, 1908, in a small farmhouse on the Pedernales River. His parents, Samuel Ealy Johnson, Jr. and Rebekah Baines, had three girls and two boys: Johnson and his brother, Sam Houston Johnson (1914–1978), and sisters Rebekah (1910–1978), Josefa (1912–1961), and Lucia (1916–1997). The nearby small town of Johnson City, Texas was named after Johnson's father's cousin, James Polk Johnson, whose forebears had moved west from Georgia. The Johnsons were originally of Scots-Irish and English royal ancestry. In school, Johnson was an awkward, talkative youth and was elected president of his 11th-grade class. He graduated from Johnson City High School in 1924.
Johnson was maternally descended from a pioneer Baptist clergyman, George Washington Baines, who pastored some eight churches in Texas as well as others in Arkansas and Louisiana. Baines was also the president of Baylor University during the American Civil War. George Baines was the grandfather of Johnson's mother, Rebekah Baines Johnson (1881–1958).
Johnson's grandfather Samuel Ealy Johnson, Sr. was raised as a Baptist. Subsequently, in his early adulthood, he became a member of the Christian Church (Disciples of Christ). In his later years he became a Christadelphian. According to Lady Bird Johnson, Johnson's father also joined the Christadelphian Church toward the end of his life. Later, as a politician Johnson was influenced in his attitude towards the Jews by the religious beliefs that his family, especially his grandfather, had shared with him (see Operation Texas).