The idea of building an airport on Saba is credited to Remy de Haenen, who brought the idea to the Saba Economic Council along with a contractor named Jacques Deldevert. De Haenen had previously made several landings of a Vought-Sikorsky OS2U seaplane off Fort Bay harbor as early as 1946. After surveying the island by air, de Haenen suggested then-privately owned Flat Point as the site for the airport. The land was cleared and graded in only a couple of weeks. On 9 February 1959, De Haenen made the first landing of an aircraft on the island, with nearly the entire population of the island in attendance.

After that first landing, De Haenen was prohibited from making further landings on the island, and there were no flights to or from Saba for several years. In the lead-up to the 1962 parliamentary elections, the lack of an airport on the island became a big issue. Sint Maarten politician Claude Wathey, who also represented Saba in the Parliament of the Netherlands Antilles, and Aruban politician Juancho Irausquin, who was at the time Minister of Finance for the Netherlands Antilles, supported the construction of an airport. The Dutch government made 600,000 guilders available to build it as part of a larger three-year plan for the Windward Islands. Irausquin told friends that during a harrowing voyage to Saba by sloop in 1960, he promised to look for funds to build an airport on the island if his life was spared.

The company contracted to build the airport was owned by Wathey's brother Chester, as well as Jacques Deldevert. On 22 March 1962, while the airport was under construction, three helicopters from the Dutch aircraft carrier HNLMS Karel Doorman landed there, marking the second time aircraft had landed on the island. Then, on 1 February 1963, a twin engine PA-23 Apache piloted by George Greaux landed on the newly asphalted runway. The airport was officially opened for service on 24 July 1963. Irausquin had died the year before and his widow cut the ribbon at the official opening ceremony on 18 September.

Greaux and several other investors formed Windward Islands Airways (Winair) in 1961, which offered service to Saba. Regular air service to Saba did not begin immediately due to the need for a STOL aircraft and the small number of people who could afford a ticket. In 1965, the airport went unused for six months. For a while, the island was served by a six-passenger STOL-capable Dornier Do 28 aircraft operated by Windward Islands Airways (Winair). The 1 December 1963, Winair timetable lists flights between Saba and Sint Maarten operated with the Do 28. Service picked up when Windward Islands Airways began flying de Havilland Canada DHC-6 Twin Otters in 1965, with the airline continuing to serve Saba with the Twin Otter as of 2024.

In 1998, Hurricane Georges destroyed the terminal building. The Dutch government funded construction of a new building, which was dedicated on 6 December 2002, to De Haenen. The propeller from De Haenen's first landing on the island is on display in the building.