He was the son of Sir Nathaniel Johnson, governor of the Province of South Carolina from 1702 to 1708, and inherited a considerable estate from his father. On April 30, 1717, he was commissioned governor of South Carolina. Like his father, he soon won the confidence of the people, but coming at a time when the powers of the proprietors were already tottering, he was baffled in his efforts to conciliate the colonists, by the proprietors' own greed and folly, and in his endeavors to sustain their authority he lost whatever influence he might have exercised.
Johnson oversaw the suppression of the pirates who were preying upon the commerce of South Carolina and neighboring colonies. Fitting out an expedition, he personally commanded a victorious engagement with them off the bar of Charleston, and carried on the campaign until they were exterminated and their famous leader Stede Bonnet was captured and executed. A month or two later Johnson is also credited with the killing of a second pirate, Richard Worley. In 1719, when the proprietary government was overthrown, the revolutionary convention, of which Arthur Middleton was president, requested him to continue in office if he would agree to administer it in the name of the king, but Johnson declined to do so, asserting the rights of the proprietors to whom he owed allegiance. James Moore II was thereupon elected governor by the convention, and Johnson was set aside. Notwithstanding the loyalty thus shown to the proprietors, he was appointed first regular royal governor of the colony in December 1729, and upon his arrival at Charleston, early in 1731, was joyfully received by the people. His administration was marked by the issuance of several acts regarding the granting of land to new settlers, and by a protracted boundary dispute with North Carolina, the two colonies being for the first time constituted entirely separate provinces. He aided James Oglethorpe in the settlement of Georgia by providing food and escort to his colonists. Johnson endeared himself to the people by his high-minded character, which won for him the title of the "good governor". He remained in office till his death, which took place in Charleston on May 3, 1735. In the same year the general assembly erected a monument to his memory in St. Philip's Church, where it remained until the edifice was burned in 1835.