Last season, Bower's Marist squad finished the year with a 12-19 record.
Bower was the general manager of the New Orleans Hornets for seven seasons before being fired in 2011. He also coached the team during the 2009-10 season, compiling a 34-39 record after coach Byron Scott was fired.
According to the report, Bower will handle the day-to-day duties of the front office.
More from Yahoo Sports:
Bower is expected to start immediately with Detroit, preparing for the draft and July free agency. The Pistons don't have a first-round pick, but they currently hold a second-round pick (No. 38 overall).SI.COM STAFF: Roundtable: 2014 NBA Finals X-Factor?
Bower was third in Executive of the Year voting in 2008, when New Orleans won 56 games and advanced to the Western Conference semifinals. In seven years as GM, the small-market franchise reached the playoffs four times. Bower played a part in drafting Chris Paul, David West and Darren Collison, as well as trading for Tyson Chandler.