He replaces Tracy Webster, who took over on an interim basis after Jerry Wainwright was fired in midseason.
Purnell was 138-88 in seven seasons at Clemson and is 394-279 in 22 years with stops at Radford, Old Dominion and Dayton. He led Clemson to the NCAA tournament the past three years, but the Tigers lost in the first round, making him 0-6 overall in that event.
For DePaul, reaching the postseason would be a major achievement after three straight losing seasons. Although the Blue Demons made 22 NCAA appearances, they haven't been there since reaching the second round under Dave Leitao in 2004.
DePaul went 8-23 this season and 1-17 in Big East play after failing to win a regular-season conference game the previous year.
Although they lost their final 13 games, the Blue Demons were more competitive after Webster replaced Wainwright in January following several blowout losses. That's little consolation for the "little school under the El tracks," as the late legendary coach Ray Meyer called it.
Athletic director Jean Lenti Ponsetto made it clear a few weeks ago that DePaul was ready to make a big splash, saying the next coach could be among the highest paid in a conference that Rick Pitino, Jim Boeheim, Bob Huggins and Jim Calhoun call home. She went with Purnell after interviewing former NBA star and Sacramento Kings coach Reggie Theus. Pittsburgh's Jamie Dixon, UCLA's Ben Howland and Chicago native Isiah Thomas also surfaced in reports.
Purnell's decision stunned the Tigers, who went 21-11 this season. He signed a two-year extension with Clemson in June and was making more than $1.3 million a year, but his buyout was only $250,000.
In a statement, Clemson athletic director Dr. Terry Don Phillips said Purnell "is one of the most respected coaches in college basketball and one of the most respected people on this campus and we hate to see him leave."
He joins a long line of Tigers coaches who have left what appeared to be a program on the rise for a challenge in a different league. Bill Foster, who led Clemson to the Elite Eight in 1980, left in 1984 to restart the basketball program at Miami. Cliff Ellis, the Tigers winningest coach, left in 1994 to go to Auburn, and Rick Barnes left for Texas in 1998 after leading Clemson to three straight NCAA tournaments.