The Louis Armstrong New Orleans International Airport is governed by the New Orleans Aviation Board (NOAB), which was created in 1943 to oversee the administration, operation, and maintenance of the new airport. The Board represents the City in all aviation matters in consultation with state, national, and international government agencies. It is an unattached board under the executive branch of the New Orleans City Government. All members of the Board are appointed by the Mayor of New Orleans with the approval of the City Council. The terms are for five years and they serve without compensation. The Chairman and Vice-Chairman are elected annually by the other Board members.

Plans for a new airport began in 1940, as evidence mounted that the older Shushan Airport (New Orleans Lakefront Airport) was too small. The airport was originally named Moisant Field after daredevil aviator John Moisant, who died in 1910 in an airplane crash on agricultural land where the airport is now located Commercial service began at Moisant Field in 1946, the terminal was a large, makeshift hangar-like building. A new terminal complex, designed by Goldstein Parham & Labouisse and Herbert A. Benson, George J. Riehl and built by J. A. Jones Company, debuted in 1959 towards the end of Mayor DeLesseps "Chep" Morrison's administration.

The original terminal was designed by Goldstein Parham & Labouisse and Herbert A. Benson, George J. Riehl and built by J. A. Jones Company, and opened in 1959. The core of this structure formed much of the facility used until November 2019. It is situated on the south side of the airfield. The terminal contained two sections, East and West, connected by a central ticketing alley. Four concourses, A, B, C and D, were attached to the terminal, and had a total of 47 gates. The vaulted arrivals lounge at the head of Concourse C and the adjacent, western half of the ticketing alley are the remaining portions of the airport's 1959 terminal complex.

When the airport terminal building opened in 1959, the name Moisant International Airport was being used for the New Orleans facility. In 1961, the name was changed to New Orleans International Airport. In July 2001, to honor the 100th anniversary of Louis Armstrong's birth (August 4, 1901), the airport's name became Louis Armstrong New Orleans International Airport.

In December 2015, the New Orleans Aviation Board, along with New Orleans Mayor Mitch Landrieu and City Council, approved a plan to build a new $598 million terminal building on the north side of the airport property with two concourses and 30 gates. Designed by world-renowned Argentine-American architect Cesar Pelli, construction on the new main terminal began in January 2016, with Hunt-Gibbs-Boh-Metro listed as the contractor at-risk. During the construction, the scope of the project was expanded so the terminal would feature 35 gates. The new terminal opened in November 2019 at a cost of $1.3 billion.

Its IATA code MSY was derived from Moisant Stock Yards, as Lakefront Airport retained the code NEW. In World War II the land became a government air base. It returned to civil control after the war and commercial service began at Moisant Field in May 1946.