Leach's hiring was announced the day after WSU Athletic Director Bill Moos disclosed Paul Wulff was dismissed after his teams went 9-40 during a four-year tenure.
"I have always admired the tradition of Washington State," Leach, 50, said. "It's a university on the move that is experiencing growth. I'm excited about what they are doing with the facilities and it's a team that has battled through some hard times and shows great promise in the future."
Leach spent 10 seasons as head coach at Texas Tech, where he employed a pass-oriented offense that carried the Red Raiders to an 84-43 record.
He was fired after an incident involving Adam James, a member of the Texas Tech team and son of former collegiate and NFL player Craig James.
Texas Tech officials said James was treated in an abusive manner after he complained of headaches during a practice session.
Leach denied the accusation and is suing the school.
"I asked ... Moos to select the best head football coach in the country and I am convinced that he has done exactly that," said Washington State President Elson S. Floyd.
Prior to his stay at Texas Tech, Leach was an offensive coordinator at Oklahoma (1999) and Kentucky (1997-98).