Huggins and the school mutually agreed to terms of a contract buyout on Wednesday, ending the coach's 16-year tenure with the Bearcats.
Kennedy had been a member of Huggins' staff the past four years. He was named an assistant coach in 2001 and was elevated to associate head coach last year.
"I am very grateful for this opportunity," Kennedy said at a news conference. "I am here, as most people are, because of Bob Huggins. I never in a million years dreamed I would be sitting here under these circumstances, but it is what it is. We all must attempt to move forward."
This will be Kennedy's first head coaching position. The Bearcats will join the Big East Conference next winter.