In 1919, Tucson opened the first municipally owned airport in the United States. In 1928 commercial flights began with Standard Airlines (later American Airlines); regular airmail service began in 1930. The 1936 airport directory shows Tucson Municipal at 32°11′N 110°55′W "just north of the railroad" (since removed) referring to the site that was then being used as the city's airport southeast of the intersection of S. Park Avenue and E. 36th Street.

During World War II the airfield was used by the United States Army Air Forces Air Technical Service Command. A contract flying school was operated by the USAAF West Coast Training Center from July 25, 1942, until September 1944.

In 1948, the Tucson Airport Authority was created as a non-profit corporation to operate the airport and oversee policy decisions. The nine member board is elected by a group of up to 115 volunteer residents from Pima County, Arizona. The airport was moved to its current location south of Valencia Road and operated on the west ramp out of three hangars vacated by World War II military manufacturing companies. A new control tower was constructed in 1958 to replace the original WWII wooden framed version.

The Tucson Airport Authority was also involved in bringing the Hughes Missile Plant, now known as Air Force Plant 44 and operated by Raytheon, to Tucson. TAA sold the land to the Hughes Aircraft Co., for the construction of the plant.

In March 1956, the Civil Aeronautics Board approved routes out of Tucson for Trans World Airlines (TWA), over opposition from American Airlines, but flights did not begin until December of that year.

In April 1957, airlines scheduled 21 departures a day: 15 American, 4 TWA, and 2 Frontier. The first jet flights were American Airlines Boeing 707s and Boeing 720s around September 1960. American began flying wide-body McDonnell Douglas DC-10s from Tucson nonstop to Dallas/Ft. Worth and to Chicago via Phoenix beginning in fall 1971 and continuing through the 1970s. In 1981, Eastern Airlines was operating direct Airbus A300 wide-body service to Atlanta via an en-route stop in Phoenix. In the late 1980s American was flying Boeing 767-200s nonstop to Dallas/Ft. Worth. The DC-10, A300, and 767 were the largest airliners ever to serve Tucson on scheduled passenger flights.

On November 15, 1963, a new terminal designed by Terry Atkinson opened with an international inspection station. The Tucson International Airport name was legitimate: Aeronaves de Mexico had begun Douglas DC-6 service to Hermosillo and beyond in 1961. In the mid-1970s successor airline Aeromexico flew McDonnell Douglas DC-9-30s nonstop to Hermosillo and on to Ciudad Obregon, Culiacan, Guadalajara and Mexico City. Bonanza Air Lines began DC-9 jet service to Mexico in the late 1960s with flights to Mazatlan, La Paz and Puerto Vallarta, and successor airlines Air West and Hughes Airwest flew DC-9s from Tucson to Mexico with their service being extended to Guadalajara, Mazatlan, La Paz and Puerto Vallarta. By late 1989, three Mexican air carriers were serving the airport: Aero California with nonstop Douglas DC-9-10 jet service from Los Cabos, Aeromexico with nonstop McDonnell Douglas DC-9-30 jet service from both Guaymas and Hermosillo, and Aviacion del Noroeste with nonstop Fokker F27 turboprop service from Hermosillo.

The terminal underwent minor remodeling during the 1960s and 1970s, and its interior was featured in the 1974 film Death Wish starring Charles Bronson.

From the early 1970s to the early 1980s Cochise Airlines was based in Tucson. This commuter airline operated Cessna 402s, Convair 440s, de Havilland Canada DHC-6 Twin Otters and Swearingen Metroliners. Cochise scheduled passenger flights to cities in Arizona and southern California.

A remodeling in 1985 doubled the size of the terminal from 150,000 to 300,000 sq ft and rebuilt the concourse into separate, two-level structures with jet bridges.

In 1987 the airport lengthened the primary runway a half-mile to the southeast for noise abatement reasons and installed arresting barriers for military planes.

A Concourse Renovation Project was finished in 2005—the last phase of a remodeling begun in 2000 that added 82,000 sq ft (7,600 m2) to ticketing and baggage claim designed by HNTB. On March 19, 2008, the previous East and West concourses and gates were renumbered with the East Concourse becoming Concourse A: Gates A1–A9, and the West Concourse becoming Concourse B: Gates B1–B11.

In 2019, the Tucson Airport became the third facility in Arizona with an ATP Flight School training center.

In January 2014, the Tucson Airport Authority board approved a no-cost, 20-year property lease with the Federal Aviation Administration for a property on which to build a new federally-funded control tower to replace the 1950s vintage tower currently in use. The new tower is located on the south side of the airport, near Aero Park Blvd.

On April 6, 2016, the Tucson Airport Authority announced the Terminal Optimization Program (TOP).