Detroit declined to trade up or down Thursday night, choosing Monroe to bolster its frontcourt.
The 6-foot-10, 225-pound Monroe averaged 16 points and nearly 10 rebounds last as a sophomore for the Hoyas.
Detroit finished last season 27-55 — its worst record since 1994 — and missed the playoffs for the first time since 2001.
The Pistons had a Top 10 pick for just the third time since Joe Dumars became president of basketball operations. The previous two were busts: Darko Milicic was drafted No. 2 overall in 2003, two years after Rodney White was taken ninth overall.