The airport was established in 1939, a year after the closure of the Aérodrome Saint-Louis. Established as a training facility for air observers, the first flight occurred on September 11, 1941. First known as the Aéroport de l'Ancienne Lorette, then the Aéroport de Sainte-Foy, and later the Aéroport de Québec, it was renamed to Aéroport international Jean-Lesage in 1993, in honour of Jean Lesage, the former Premier of Quebec. The airport is managed and operated by Aéroport de Québec inc., a non-profit and non-share corporation.

Beginning in 2006, with a budget of $65.8 million, Québec/Jean Lesage International Airport underwent a modernization designed to increase the terminal's capacity and substantially enhance the level of passenger service. The modernization included reconfiguring the terminal on two levels, restructuring the baggage handling area and arrivals area, and reconfiguring and enlargement of the waiting rooms. Fifty-four percent of the financing was provided directly by Aéroport de Québec inc. Completed in June 2008, the new configuration of the airport enabled it to handle 1.4 million passengers a year.

Based on the passenger figures for 2009 and 2010, it became clear that the terminal building would reach its design capacity by 2012. Aéroport de Québec inc. therefore began planning further investments of nearly $300 million to expand the terminal building again. On July 4, 2011, work began on the second phase of the airport expansion, which lasted until 2017. Partially funded through an Airport Improvement Fee, the terminal building was doubled in size, at a cost of $224.8 million. The work included expanding the international facilities, redoing runways, changing and upgrading the layout of the taxiways, and enhancing customer service facilities.

On September 19, 2013, because of earth magnetic north pole drift, runway 12/30 was renamed to runway 11/29.

On 10 March 2016, Prime Minister Justin Trudeau and President Barack Obama announced the addition of the airport to the list of Canadian airports containing U.S. border preclearance facilities. In 2019, Trudeau and President Donald Trump also announced that the airport would obtain border preclearance. However, as of March 2024, preclearance is not yet available.

On December 11, 2017, the first phase of YQB2018, the expansion project, was completed with the opening of the new international terminal. Features included more dedicated baggage carousels serving international flights, a new customs area, an expanded food court and restaurant area, four new gates (34 to 37), an improved and larger loading area for cars and buses, and a larger capacity baggage area.

The last expansion phase, which involved linking the domestic and international terminals, was completed in the summer of 2019.