Brendan Mullins, Bryan's older brother who has been an assistant coach at Illinois State for the last two years, will help lead the Salukis in 2019-20.
The Redbirds went 18-15 in his first season but reached the title game of the Missouri Valley Conference tournament, where they lost to Loyola.
Illinois State went 17-16 this past season, falling into the opening round of the league tournament for the first time in head coach Dan Muller's career. The Redbirds beat Evansville and then lost to second-seeded Drake in the tournament quarterfinals.
"Brendan represents everything I want this program to stand for," Bryan Mullins said in a statement.