The game will be held April 27 at the Ford Center at The Star and will be broadcast on CBS at 7 p.m.
"The Alliance has built a foundation of high-quality football, revolutionary technology and world-class partnerships with the NFL, CBS and Turner Sports," Dallas Cowboys owner Jerry Jones said in a news release. "It was only natural that we at the Cowboys organization would want to join that great group of partners."
The game will take place on the same weekend as the Dallas Cowboys' NFL Draft festivities.
Jones is a friend of the league and its executives, Bill Polian, head of football for AAF, said in a news release.
"To be able to showcase our brand of top-flight football on NFL Draft weekend in the state-of-the-art football facility built by Jerry is a Texas-sized win for our league," he said.
Fans who purchased tickets for the Las Vegas game will receive full refunds. Tickets for the 2019 Alliance Championship will go on sale April 2 at www.aaf.com.
The AAF is a new professional football league in its inaugural season. Made up of eight teams, the league plays during the NFL's offseason and includes local and developing football talent.