The airstrip was built by the U.S. military in 1956, in order to support a DYE Station, part of the Distant Early Warning Line. The DYE-4 station is located on the south tip of Kulusuk Island, linked by a 8 km (5 mi) road. The U.S. departed the site and airport in 1991. Many remnants of the US military use of the field remain, including vehicles and plant used by the military to maintain the strip. Like some other airports in Greenland it was not built at a location suitable for civilian travel, i.e. not near the local major settlement. Helicopters are used for the local transfer, as there is too much ice for boats during parts of the year. There are political discussions on building a new airport at Tasiilaq, a major settlement in the region, and close to Kulusuk Airport.

During an operation in the early 1990s Kulusuk Airport was the base of operations for a team attempting to recover a US Air Force Lockheed P-38 Lightning from a glacier approximately 80 miles away. The aircraft was originally part of a flight of 6 P-38 and 2 B-17 bombers taking part in Operation Bolero during WW2. The team recovered a P-38 in 1992 and when rebuilt to flying condition the aircraft was named Glacier Girl. The story of its recovery is displayed on the wall inside the departures hall.

Air Alpha operated helicopter flights on-demand by two Bell 212 helicopters in the 1990s to early 2000s. Air Greenland later assumed responsibility of helicopter flights.

After the U.S. left the airport, in 1992 work began on a new terminal building and associated service buildings to replace a 200 m2 shed previously in use. It was designed by Icelandic architect Sveinn Ívarsson of Arkítektastofan sf. in cooperation with Verkfræðistofa FHG and constructed by C.G. Jensen of Denmark. The new terminal opened in December 1994.

In 1959, Icelandair began operating day trips during the summer to Kulusuk from Reykjavík Airport operated using Fokker F27 Friendship aircraft, arriving in the morning and departing in the evening. This created an influx of day-tripping tourists and a small tourism industry was created in Kulusuk. Icelandair ceased offering day trips in 2019, but continues to serve the airport with a more conventional flight schedule. Kulusuk Airport has, in cooperation with Icelandair, installed de-icing facilities since the winter of 2014–2015.

In 2023, flights were moved from the downtown Reykjavík Airport to the larger Keflavík Airport, to improve onward connections. From 2025, Icelandair reduced its service to serve Kulusuk seasonally only during summer, which was criticised by locals in Kulusuk.