Padgett was a part-time starter for the Jayhawks last season, averaging 6.5 points and 4.5 rebounds. He announced his decision to transfer on April 15.
"David is someone we can build our offenses and defenses around for next year when we enter the Big East," Coach Rick Pitino said. "He can do it all as a big man. He runs the floor, he can spot up, he blocks shots and he rebounds. He also has a passion to eat, sleep and drink the game of basketball."
Padgett's addition boosts a Cardinals frontcourt that struggled. He will form the nucleus along with Francisco Garcia and Taquan Dean that should be a top-15 team.