Petersen, 49, just completed his eighth season at Boise State with an 8-4 record. Overall he was 92-12 with five bowl game victories while at Boise State. The Broncos won five conference titles during Petersen's time as coach.
He takes over at Washington for Steve Sarkisian, who last week became the coach at Southern California.
"On behalf of the University of Washington and the entire Husky Nation, I am proud to welcome Chris Petersen as our new head football coach," Washington Athletic Director Scott Woodward said in a statement.
"Coach Petersen's success and record are extraordinary, but even more impressive is the man himself. His integrity, work ethic and character make him an outstanding fit and leader of our student-athletes at UW.
"We are thrilled and proud to call Coach Petersen a Husky."