The school said Kennedy has signed a six-year contact.
Kennedy, who was the heavy favorite to get the job, has experience with the program, having played and coached in Birmingham. Kennedy played three seasons at UAB (1988-91), leaving as the program's second all-time leading scorer. He spent six seasons as an assistant coach for the Blazers (1995-2001).
"I am blessed to be able to return to my alma mater, in a city that I love, to lead this storied basketball program," Kennedy said in a statement.
Kennedy stepped down from Ole Miss toward the end of the 2017-18 season, his 12th season in charge of the Rebels. While in Oxford, Kennedy went to two NCAA tournaments and won 20-plus games nine times.
"Andy is a proven winner both as a player and a coach, and we are elated to have him lead our men's basketball program," athletic director Mark Ingram said in a statement. "He helped build UAB basketball's proud tradition as one of the best to ever play here, and I am confident he will elevate the program to new heights as our coach."
Kennedy's hire is still pending approval by the University of Alabama System board of trustees.
Kennedy, 52, has spent the past two seasons as a college basketball analyst for ESPN.
He will replace Rob Ehsan, who was fired last week after four seasons at the helm.