The acquisition of land where Alicante-Elche Miguel Hernández Airport now stands began in November 1964, and the construction of a 2,700-metre runway, a taxiway, rapid exit taxiways and an ILS installation began a few months later.

On May 4 1967, the new Alicante Airport opened to national and international passenger and cargo traffic and, at the same time, La Rabassa aerodrome was closed. The first aeroplane, an Aviaco Convair Metropolitan, landed that same day. Iberia joined the airport traffic in November, 1969 with Alicante-Madrid and Alicante-Barcelona routes.

Traffic increased immediately, as all the tourists who previously flew to Valencia to reach Alicante coast destinations, now began to fly into Alicante Airport.

In 1970 the number of passengers was close to one million and it became necessary to build a new passenger terminal, the first phase of which was inaugurated in June, 1972. The new building was used only for international flights. The second phase was completed in 1974, and national traffic was incorporated in March, 1975.

Sustained growth in traffic reached two million passengers in 1978, making it necessary to reform the passenger terminal and extend aircraft parking by 60,000 square metres. For operational reasons, the length of the runway was extended by 3,000 metres.

In 1996 an extensive refurbishment was undertaken in order to be able attend in a short time the nine million passengers using these facilities each year Five airbridges were installed for boarding and a new office building for airline companies was built, as well as an operations centre and a business centre. Car parking capacity was also increased, a new exit was built at header 28 and the plane apron was extended.

In March 2011, the New Terminal Area was opened, capable of handling nearly 6,000 passengers per hour and 20 million passengers per year; it includes a new terminal building, a boarding dock, a car park building, new access roads, and an extended aircraft parking apron and taxiway.