Mack had enrolled in summer school at the University of New Orleans but left after one week of classes, a report on the Memphis Web site said.
"I'm happy for Doneal, and I'm proud of our university for allowing him to return," Calipari said. "When working with kids, they sometimes make illogical decisions. Once again, our administration steps up and does the right thing by letting this young man return and attend this great university."
Mack was on the 2007-08 Memphis team that won an NCAA-record 38 games (38-2). The Tigers made it to the NCAA Tournament championship game, where they lost to Kansas.