The first Savannah Municipal Airport was opened on September 20, 1929, with the inauguration of air service between New York City and Miami by Eastern Air Express. In 1932, a city resolution named the airport Hunter Field. A trolley car was used as the first terminal at Hunter Field in the mid-1930s. In 1940, the U.S. Army Air Corps proposed to take over Hunter Field if a war started. While commercial airlines continued to use Hunter Field, the city decided to build a second municipal airport in response to the increased military presence.

The City of Savannah acquired a 600-acre tract near Cherokee Hill, one of the highest elevations in the county, and construction of a new airfield began under a Works Progress Administration project. Three 3,600-foot runways were constructed running north–south, east–west, and northeast–southwest. In 1942, before the completion of this new airfield, the U.S. Army Air Corps decided to take over the new facility and start additional construction to carry out its mission. It named the airfield Chatham Field and used it until the end of World War II as a bomber base and crew training base for B-24 bombers as well as fighter aircraft.

In 1948, Chatham Army Airfield was turned over to the Georgia Air National Guard and the airport was renamed Travis Field, in honor of Savannah native Brigadier General Robert F. Travis, killed in the crash of a B-29 bomber near Fairfield-Suisun AFB, California, and his brother, Colonel William Travis. To accommodate the airlines, Travis Field received a new control tower and an airline terminal in the former base theater.

In 1958, work began on a new airline terminal. In 1962, an additional extension brought the east–west runway's length to 9,000 ft (2,700 m). The jet age arrived in 1965 when Delta Air Lines introduced Douglas DC-9-10 flights. Grumman Aircraft opened a $7.5 million Gulfstream manufacturing plant at Travis in 1967. A new $21-million terminal building was built on the northwest corner of the airport in 1994.

A six-gate terminal built-in 1960 was replaced in 1994 by the current facility, part of an overall $74 million renovation of the airport. Although the airport had no direct international flights at the time, it was renamed Savannah International Airport in 1983, then Savannah/Hilton Head International Airport in 2003.

In 1992, the airport had international service with non-stop flights to destinations in the Caribbean and Mexico when Key Airlines was operating a passenger hub in Savannah. Key Airlines also operated non-stop mainline jet service to a number of U.S. cities at this time and from Savannah. According to the Key Airlines system timetable dated October 1, 1992, non-stop services primarily operated with Boeing 727-100 and 727-200 jetliners were being flown from the airport to Antigua (ANU), Aruba (AUA), Atlanta (ATL), Baltimore (BWI), Boston (BOS), Cancun (CUN), Chicago Midway Airport (MDW), Cozumel (CZM), Curaçao (CUR), Freeport (FPO), Montego Bay (MBJ), Nassau (NAS), New York Newark Airport (EWR), Orlando (MCO), St. Maarten (SXM) and St. Thomas (STT). In addition to these non-stop flights, a one-stop direct service was also flown by the airline from Savannah to St. Croix (STX). Key Airlines subsequently experienced financial difficulties and then ceased all flights in 1993.

Some 3,680 feet (1,120 m) from the west end of Runway 10 (the main east–west runway) are two concrete grave markers. A runway extension project placed the runway through a small family plot and the graves of the airport property's two original owners. Because the family did not want to remove and relocate the graves, the markers were placed on the asphalt runway. Runway 10 is thought to be the only airport runway in the United States with marked gravestones in it. Federal law generally prohibits the moving of a grave without the permission of the next of kin. In this case, two graves of the Dotson Family, the earliest grave dating back to 1857, were encountered during the construction of the runway. Since the next of kin could not be located, the graves were left undisturbed. Two additional graves are located off the runway surface.

The new 275,000-sq.-ft. terminal opened in May 1994 with eight gates (expandable to 19 gates). The project included new roads, a new aircraft taxiway and parking apron, stormwater ponds, landscaping, and a new interchange at I-95 for entry into the Airport (Exit 104) at mile marker 104. The total cost for the project was $68.5 million. It was completed one month ahead of schedule and under budget. It was designed by KBJ Architects.

A terminal expansion project was completed in July 2007, adding five departure gates (for a total of 15).