Construction of the airport began in November 2003 following the removal of Saddam Hussein, with the foundation stone laid that month. It was officially opened by Jalal Talabani, who was back then the president of Iraq, on 20 July 2005, under the name Sulaymaniyah International Airport. Several months after its opening, on 2 November 2005, the airport received international recognition from the International Civil Aviation Organization (ICAO).

International flights were shut down from 29 September 2017 following a decision by the Iraq Civil Aviation Authority (ICAA) due to the 2017 Iraqi–Kurdish conflict, but the airport remained open for domestic and humanitarian flights. The international flights ban was lifted in March 2018 by Haider Al-Abadi. The airport has been operated by the Iraqi government following the 2017 ban.

In September 2025, Sulaymaniyah International Airport was officially renamed Jalal Talabani International Airport, in honor of the late Jalal Talabani, former President of Iraq and a prominent Kurdish leader. The renaming followed a proposal from the Jalal Talabani Foundation, which had pursued the change for over four years. The proposal was approved by the Iraqi Council of Ministers and Prime Minister Mohammed Shia al-Sudani. The name change officially took effect on 19 March 2026, following a decision by the Iraqi Civil Aviation Authority (ICAA). From that day on, the new designation was adopted in all official correspondence, aeronautical charts, and related technical documentation. Airport officials described the renaming as a “historic event” honoring Jalal Talabani’s legacy.