Johnson was born on 13 June 1782 on John's Island, South Carolina, near Charleston and was educated at home in Georgetown, South Carolina by his mother and by private tutors. His mother was of the Particular Baptist faith, believing that the redemptive work of Christ only applied to those who were saved. As a child he met President George Washington and Dr. Richard Furman, pastor of the First Baptist Church Charleston, who made a great impression on him. He attended Brown University, receiving a degree in 1804. He had intended to become a lawyer, but was converted during a Baptist revival in 1804, and devoted the rest of his life to Christian service. He married Henrietta Hornby in 1803. One of their eight children who reached maturity, Francis C. Johnson, became a Southern Baptist missionary to China in 1846.
After preaching in several churches from 1804 to 1806, Johnson was appointed pastor of the Baptist church at Euhaw near Beaufort, South Carolina. In October 1809 he baptized five new converts in the Congaree River in Columbia, SC. Later that day he organized First Baptist Church Columbia with these 5 new converts and 7 other local Baptists, under the leadership of Jonathan Maxcy, first president of the University of South Carolina and ordained Baptist preacher. In 1810 he was invited to become chaplain of South Carolina College, Columbia. In 1811 he accepted an offer to become pastor of the Baptist church in Savannah, Georgia. It was here that Johnson met Luther Rice, who interested him in foreign missions, and whom he helped arrange the General Missionary Convention of the Baptist Denomination in the United States of America for Foreign Missions, or Triennial Convention, in 1814. He was one of the framers of the constitution of this convention.
Returning to South Carolina, after serving again as pastor of the Columbia church Johnson moved to Greenville, South Carolina where he was principal of Greenville Female Academy, and founded a Baptist church in the town. Johnson was one of nine men who formed the South Carolina State Baptist Convention in 1821. He succeeded Richard Furman as president of the convention and served from 1825 to 1852. In 1830 he moved to Edgefield to become principal of Edgefield Female Academy and pastor of Edgefield Baptist Church.
Johnson became the last southern president of the General Missionary Convention of the Baptist Denomination in the United States of America for Foreign Missions between 1841 and 1844. As tensions grew between the northern and southern Baptists over the issue of slavery, he attempted to avoid a split but in 1845 was asked become first president of the breakaway Southern Baptists Convention, serving until 1851. In this role he helped found the Furman University, which became Southern Baptist Theological Seminary in 1859, based in Greenville, South Carolina. Towards the end of his life he was chancellor of Johnson Female University, Anderson, South Carolina (1853–58).