Clifton Woodrow Brannon was born to George Wesley and Beulah Green Brannon on April 14, 1912, in Fitzgerald, Georgia. When George Brannon died, Clift became the chief support of his family which included six brothers and sisters. After graduation from high school in 1929, Brannon attended Georgia School of Technology and Woodrow Wilson College of Law in Atlanta, Georgia. He was admitted to the practice of law in Atlanta in 1932.

On February 16, 1935, he was married to Ola Ruth Hall of Winder, Georgia. The Brannons had three children, Beverly Mae, Madlyn Sue, and Clifton Woodrow. Brannon became an attorney for Home Owners' Corporation in 1933, a position he held through 1935. Between 1940 and 1949, he was general counsel for R. G. LeTourneau, Inc. and the LeTourneau Foundation. His law practice in Longview, Texas, began in 1946 and continued until 1949.

Concurrent with his career as a lawyer, Brannon became increasingly involved as a lay preacher. He had joined the Methodist Church in 1923, and experienced conversion in 1932 through his mother's influence. He preached his first sermon in 1932. He was licensed to preach by the North Georgia Conference Methodist Episcopal Church South in 1933, and attended Atlanta Bible Institute in 1934. In 1940, he was appointed general counsel and director of Winona Lake Christian Assembly, Inc., Indiana, for which he prepared a charter. He served in this capacity between 1940 and 1949.

Brannon conducted revivals yearly between 1933 and 1949 and was a supply pastor between 1942 and 1946. In 1945, he was ordained to the ministry and became Vice President of the Baptist Brotherhood Convention of Texas, a position he held between 1947-1948. He was President for the 1949-1950 term.

His first radio broadcast was held in 1938, and he subsequently broadcast two hundred consecutive weekly one-hour programs from radio station Whosoever Heareth, Inc., between 1942-1946. The first broadcast was in October 1942, from the Level Grove Baptist Church in Cornelia, Georgia, aimed at providing rural residents with a substitute for church services where there were none. The station opened while Brannon was a layman and working deacon of the First Baptist Church in Toccoa, Georgia. On Brannon's invitation, Billy Graham spoke several times on the Whosoever Heareth Hour in 1945.

Brannon became a full-time evangelist for the Southern Baptist Church in 1949, a career which included a radio and TV ministry. He received an LL.D. from Burton Theological Seminary, and since 1949 has conducted revivals in at least thirty-eight countries on three continents. He was Vice President and Director of All India Prayer Fellowship, Inc., in 1973, and became President of Clift Brannon Evangelistic Association in 1974. Other positions he held included member of the Board of Directors of Word for World Crusade, Universal Concern Foundation, past President of Texas Baptist Brotherhood Convention, Vice President of the Southern Baptist Convention, and President of the Conference of Southern Baptist Evangelists.

In his work of evangelism, Brannon developed an edition of the New Testament to be used by workers in individual evangelism. Soul Winner's New Testament, King James Version, was first published in 1959 with Brannon as editor. Other editions included an American Standard translation, 1972, Soul Winner's Living Bible New Testament, 1973, and The Guide to God New Testament, 1974.

In 1974, Whosoever Heareth, Inc., transferred rights to the Clift Brannon Evangelistic Association, Inc., which scheduled the activities of Brannon and his wife. Whosoever Heareth became a Foundation for paying designated expenses and distributing Soul Winner's New Testaments world-wide.