Pachulia averaged 5.4 points and 4.7 rebounds per game in 69 appearances for Golden State last season.
Bradley began last season with the Pistons before he was sent to the Clippers as part of the Blake Griffin trade.
The Detroit Pistons have named Dwane Casey as Stan Van Gundy's long-term replacement.
Casey was fired by the Raptors after they finished 59-23 this past season.
The Detroit Pistons hit a wall after Blake Griffin's arrival provided a boost and Rex Walters pointed the finger at the Los Angeles Clippers
The Pistons won their first five games with Blake Griffin on their roster, but then they lost 10 of their next 12.
The veteran coach said he's excited about coaching the Wolverines "next season and in the years to come".
Casey posted a 320-238 record in seven seasons with the Raptors while Beilein has been at Michigan since 2008-09.
Fired coach Stan Van Gundy also held the title of president as well as head coach, and Bower was his top lieutenant.
Beilein, 65, has spent his entire coaching career in the college ranks.