Standiford Field was built by the Army Corps of Engineers in 1941 on a parcel of land south of Louisville that was found not to have flooded during the Ohio River flood of 1937. It was named for Dr. Elisha David Standiford, a local businessman and politician, who was active in transportation issues and owned part of the land. The field remained under Army control until 1947, when it was turned over to the Louisville Air Board for commercial operations.

Until around 1947, Bowman Field was Louisville's main airport, which was too close to downtown to expand. For many years, passenger traffic went through the small brick Lee Terminal at Standiford Field. Today's more modern and much larger facilities were built in the 1980s. Most of the Lee Terminal was later torn down.

When Standiford Field was built by the U.S. Army Corps of Engineers in 1941, it had one 4,000-foot (1,200 m) runway. The airfield opened to the public in 1947 and all commercial service from Bowman Field moved to Standiford Field. American, Eastern, and TWA were the first airlines and had 1,300 passengers a week. The airlines used World War II barracks on the east side of the field until May 25, 1950, when a proper terminal opened. Lee Terminal could handle 150,000 passengers annually and included 6 new gates, which increased terminal space to 114,420 square feet (10,630 m2). The three runways (1, 6 and 11) were all 5000 ft.

The April 1957 Official Airline Guide shows 45 weekday departures on Eastern Airlines, 19 American, 9 TWA, 4 Piedmont and 2 Ozark. Scheduled jet flights (Eastern 720s to Idlewild) began in January–February 1962.

In 1970, the terminal again expanded; the main lobby was extended and the 33,000-square-foot (3,100 m2) Delta Air Lines concourse was built.

The 1980s brought plans for a new terminal, the Louisville Airport Improvement plan (LAIP). Construction of a new landside terminal designed by Bickel-Gibson Associated Architects Inc. began, costing $35 million with capacity for nearly 2 million passengers in 1985. Parallel runways, needed for expanded UPS operations, were part of the airport expansion. Most of the improvements were completed in the 1990s and the airport was totally renewed.

During the 1990s, Southwest Airlines began service to the airport which helped passenger boardings increase 97.3 percent. In 1995, the airport's name was changed from Standiford Field to Louisville International Airport. Around that time, SDF opened the two new parallel runways: runway 17L/35R, 8,578 feet (2,615 m) long and runway 17R/35L, 11,887 feet (3,623 m); both are 150 feet (46 m) wide. The Kentucky Air National Guard moved its base to SDF with 8 military aircraft; a new UPS air mail facility, new corporate hangars, a four-level parking garage and a new control tower were also added. A new FBO was added, run by Atlantic Aviation and managed by Michael Perry.

In 2005, a $26 million terminal renovation designed by Gensler Inc. was completed. As of 2024, the airport is in the midst of a major renovation project called SDF Next, which includes more than $1 billion in planned enhancements to the Jerry E. Abramson Terminal, work on the baggage claim, updates to security and lighting, and changes to the rental car counters, among other improvements.

On January 16, 2019, the Louisville Regional Airport Authority voted to change the name of the airport to Louisville Muhammad Ali International Airport in honor of the boxer and Louisville native Muhammad Ali. On June 6, 2019, the airport unveiled its new logo, featuring "Ali's silhouette, arms up and victorious, against the background of a butterfly".