The 6-foot-3, 160-pound Levitch is considered one of the top shooters in the state of Kentucky among Class of 2013 prospects.
Levitch was getting looks by several other schools but said when he heard a walk-on spot was possible at U of L that ended any other options.
"I first heard (it was possible) when we were at (AAU) Nationals in Orlando (in July)," Levitch said. "When we got back from Florida, I met with coach (Rick) Pitino and he told me the opportunity was on the table.
"I thought about it for two or three days and told him I would do it. It's such a great opportunity for me and I still can't believe it. It's pretty crazy to think I am going to be part of the U of L team. Obviously, I know I need to add some strength but it's just a great honor for me."
Levitch averaged 18.8 points, 4.2 assists and 3.2 rebounds a game as a junior for the Mustangs. He hit 42.3 percent from three-point range.
"David shoots the ball well," Pitino said. "As he gains more strength, like (current walk-on Tim) Henderson, he will be a great addition to Cardinal Basketball."
Levitch was an All-Eighth Region performer and has already scored more than 1,000 points during his career.