The airport was created in the 1930s as the best place to put an airport in Teton County. The airport was designated as part of a national monument in 1943 and merged with Grand Teton National Park in 1950. The runway was extended to its current length in 1959. President John F. Kennedy landed in an Army helicopter here on September 25, 1963. During the 1960s and 1970s an extension of the runway to 8,000 feet (2,400 m) was considered to accommodate jet aircraft, but the National Park Service successfully opposed the plan. In the late 1970s jets began using the existing runway. The area is noise sensitive and the airport allows no jets louder than stage III. The airport is an important habitat for the rare sage grouse during its mating season.

The original Frontier Airlines was the first carrier to serve Jackson Hole, starting in 1959 with routes to Denver, Salt Lake City, and Billings using Douglas DC-3s, and later the Convair 340 and 580. This was eventually upgraded to the Boeing 737-200 series aircraft shortly before the airline shut down in 1986 following the Airline Deregulation Act. Other than some commuter airlines that briefly served the airport, Frontier had the only service until Western Airlines began flights to Salt Lake City in 1983 using Boeing 737-200s. Since that time, the airport has also seen service from Continental Airlines, Northwest Airlines, Horizon Air, Big Sky Airlines, and Southwest Airlines in the past as well as many other commuter carriers.

The airport once had an unusual terminal resembling a pioneer log cabin. The terminal was completely rebuilt between 2009 and 2014. The new terminal, designed by Gensler, still blends with the unique surroundings of the national park with exposed wood, fireplaces, and nature photography throughout. The park limited the height of the terminal building to 18 feet (5.5 m). The terminal design received an American Institute of Architects Honor Award in 2014. In the spring of 2021, construction began on relocating the pre-security Café to baggage claim. This relocation created additional check-in counter space for Allegiant Airlines. In 2021, Allegiant left the airport due to small flight loads and the inability to reliably turn a profit at the airport. The next phase of construction will modernize and expand the TSA checkpoint and give more gate space to American Airlines. In the spring of 2022 when the airport is closed, construction will commence on rebuilding Jedediah's restaurant and adding two more gates.

Between 2001 and 2023, Jackson Hole Airport employed its security screeners under contract with the Transportation Security Administration's Screening Partnership Program, and was the only airport that directly employed its security screeners. Airport screening operations transitioned to the TSA in May 2023.