On 5 October 1921, the first aircraft landed at Alice Springs, near the site where Eddie Connellen would later establish an aerodrome and founded Connellan Airways (later to become Connair) in 1939. As the town grew, the airport, known locally as "townsite aerodrome" was unable to handler larger and heavier aircraft.

The present airport, originally Seven Mile Aerodrome, was originally built in 1940 by the Australian Department of Defence and was used primarily by the Royal Australian Air Force. The airport became an important staging point for military aircraft supporting the allied campaign in the Dutch East Indies, and was an operational RAAF base from 1942 until 1946. No. 57 Operational Base Unit (RAAF) ran and maintained the aerodrome.

After the war, most civilian operations transferred to the Seven Mile Aerodrome. Trans-Australia Airlines began a weekly Douglas DC-3 flight between Alice Springs and Adelaide in November 1947. Weekly Ansett flights to Melbourne commenced in 1960, while TAA established a permanent presence in Alice Springs from 1961. Connellan Airways continued to operate out of their own facilities at the townsite aerodrome until 1968, which is now the site of the Central Australian Aviation Museum.

In 1958, it was officially renamed Alice Springs Airport. The terminal moved to the current site in 1964, the same year the airport's fire station was built. Both opened in 1965 The main runway was extended to its present length of 2,438 m (7,999 ft) in 1961. A new control tower was completed in 1969, coinciding with the closure of the townsite aerodrome and remaining traffic there moving to the main Alice Springs Airport.

Frequent visitor to Alice Springs, British businessman Alistair McAlpine (1942–2014), wrote in his memoir of the impression the new airport had on him in a May 1994 visit:

Only when I climbed down the airport steps did I begin to think I had come to the wrong place. A sign said 'International Airport' and that is what I saw. Gone were the collection of buildings stitched together that had passed for a terminal. In front of me was the modern airport building–there was no longer a grubby bar with grubby customers where sweat and stubble mixed with ice-cold beer; the flies had gone too. The cafeteria could seat a hundred and needed to, for planes arrived every few minutes instead of once or twice a day (..) The days when the population of 'The Alice' came to the airport for a beer and to wonder at the miracle of flight are long gone.

Units based at Seven Mile Aerodrome

No. 57 Operational Base Unit RAAF ran and maintained the between 1941 and 1946.

Elements of No. 87 Squadron RAAF were based at the aerodrome for a short period to undertake aerial topographic survey work after World War II.

Asia Pacific Aircraft Storage

On 27 May 2011, it was announced that Alice Springs Airport had been selected to be the first large-scale aircraft boneyard outside the United States.

The facility, which commenced operation in June 2014, is operated by Asia Pacific Aircraft Storage Ltd. The dry arid climate of Alice Springs is similar to Arizona, a major hub for aircraft storage and preservation. The facility is designed to store commercial aircraft not in use, as well as stripping and recycling retired aircraft components.

On 30 September 2020, it was announced that the facility was close to its current capacity and would be expanded from around 100 aircraft to up to 200 aircraft. At the height of the pandemic, 152 aircraft were stored at Alice Springs, the last returning to operational service with Cathay Pacific in June 2024.