The school said Wright was introduced at a news conference on campus Tuesday.
He takes over for Jim Molinari, who resigned last week.
Wright was Molinari's associate head coach before moving to Ball State as an assistant last season.
The Leathernecks were 10-20 last season.
Molinari took Western Illinois to its only two post-season appearances as a Division I team. The Leathernecks went to the CBI tournament in 2012 and 2013.