Mack's father said last month his son would be transferring after two seasons with the Tigers because he wanted more playing time.
Memphis said in a news release Friday that Mack enrolled in summer school at the University of New Orleans, but withdrew after one week of classes.
Calipari says he is happy for Mack. He says students sometimes make "illogical decisions" and the school's administration did the right thing by allowing Mack to return.
Last season Mack played 39 games, averaging 6.9 points and 1.6 rebounds.