In 1928, the Charleston Airport Corporation was founded and purchased 700 acres (280 ha) of land previously belonging to a mining company. Although privately developed at first, the City of Charleston floated bonds in 1931 to acquire a portion of the site for passenger service. Within ten years, three runways were paved and outfitted with lighting for nighttime operations. In World War II, control of the airfield passed to the United States Army though civilian service was allowed to continue to use the airfield. After the war, the airfield reverted to civilian use for a short time. In 1949, a new passenger terminal was built.

During the Korean War, the airfield was reactivated for military use and in 1952, the City of Charleston and the United States Air Force reached an agreement on control of the base and the runways—an arrangement that has been renegotiated over time and that continues to this day. In 1979, the civilian portions of the airport were transferred from the City of Charleston to the Charleston County Aviation Authority, which had operated two other airports in the area. The current terminal on the south end of the airport was built in the 1980s on land acquired by Georgia Pacific.

In October 2009, Boeing announced that it would build a major plant on 265 acres (107 ha) at the airport as a second final assembly site for its 787 Dreamliner commercial aircraft. The facility began limited operations in July 2011 and rolled out its first completed aircraft in April 2012. Additional facilities to complement aircraft assembly have since been announced by the company.

Since 2010, the airport's passenger figures have doubled. New services established by additional airlines during this time along with increased services from the three legacy carriers have contributed to this growth.

In 2021, the newly established Breeze Airways announced that the airport would serve as a focus city for the airline and announced service to 11 cities. In 2022, the airport authority announced a 20-year master plan for future growth of the airport, including the constructing of an additional concourse, adding up to 11 new gates, providing additional plane stands, and expanding parking facilities for vehicles.

The airport has had brief periods of international service. In 2001, Air Canada briefly served the airport from Toronto but ended service immediately after the September 11th attacks in 2001. Porter Airlines briefly served Charleston with flights to Toronto in 2015. In April 2019, British Airways launched a seasonal route to London's Heathrow Airport. This was Charleston's first transatlantic flight. The first season ended in October. Due to the COVID-19 pandemic, the service was suspended in 2020. In 2023, Air Canada announced a return to Charleston with daily nonstop flights to Toronto starting in March 2024.