Phelps replaces Keno Davis, who left Drake to take over at Providence. Drake was 28-5 last season and won the Missouri Valley Conference regular-season and tournament championships.
"I consider it an honor and privilege to be named the head coach at Drake University," said Phelps. "President (David) Maxwell has fostered a true family environment where the 'Drake experience' is a special one for students, faculty, staff and the entire Drake community.
Phelps was an assistant at North Carolina State from 1996-2006 under head coach Herb Sendek and moved to Arizona State with Sendek in 2006.