Gleason has spent the past five years as associate head coach at Seattle and previously spent 12 years as head coach at Humboldt State.
She replaces Wendy Schuller, who spent 20 years as Eastern Washington's head coach and was fired after three straight losing seasons.
During Gleason's tenure at Seattle, the Redhawks were in the top three in scoring offense in the Western Athletic Conference three times.
At Division II Humboldt State, Gleason compiled an overall record of 201-137 and was the program's all-time winningest coach upon her departure.
She is a graduate of California State-Chico.