By 1998, the Dallas Mavericks, then owned by H. Ross Perot Jr. and the Dallas Stars were indicating their desire for a new arena to replace the aging and undersized Reunion Arena. Dallas taxpayers approved a new hotel tax and rental car tax to pay for a new arena to cover a portion of the funding, with the two benefiting teams, the Mavericks and the Stars, picking up the remaining costs, including cost overruns. The new arena was to be built just north of Woodall Rodgers Freeway near Interstate 35E on the site of an old power plant.

On March 18, 1999, American Airlines (AA) announced that it would be acquiring the naming rights for the arena for US$195 million. AA is headquartered in nearby Fort Worth and is based at Dallas/Fort Worth International Airport. From its opening in 2001 until 2013, the AAC had the then-current AA logo; thereafter the AAC has used the current AA logo.

The first event occurred the next day with an Eagles concert. Outdoors on the plaza before the Eagles concert, Tom Chaffee & the Saturnalia instrumental rock in jazz band played while patrons entered the venue. On the next night, the arena hosted the last show of Michael Flatley's Feet of Flames tour. The first sporting event took place on August 19, 2001, with the Dallas Sidekicks of the World Indoor Soccer League taking on the San Diego Sockers.

The AAC includes a practice court for the Mavericks, who used it for regular practices until 2017 when a separate facility was built in the Dallas Design District near the arena.

The Mavericks' lease on the AAC runs through to 2031, and once it runs out owner Mark Cuban has considered a new arena to replace the AAC.

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