Johnson was born in St. James Goose Creek Parish (now part of Berkeley County, South Carolina) to William Johnson Sr., a blacksmith who moved to South Carolina from New York, and Sarah Johnson, née Nightingale. Both of his parents were supporters of the American Revolution. During the Revolution, Johnson Sr. was considered by British authorities to be "one of the most dangerous and important of the rebels." He led Charleston revolutionaries alongside Christopher Gadsden and was the originator of Charleston's Liberty Tree. Following the Siege of Charleston, both Johnson Sr. and Gadsden were imprisoned in St. Augustine, Florida by British commander Sir Henry Clinton. Johnson Jr., alongside his brother and mother (who was also a revolutionary), subsequently fled to New York City, where they lived for the remainder of the Revolution. Following the war, Johnson Sr. was a representative for Charleston in the South Carolina General Assembly.