Leach has been out of coaching the past two seasons. During that time he has put out two books, worked in television and hosted a satellite radio show.
Wulff was fired after going 9-40 in four years during which he was charged with rebuilding a downtrodden football program. The Cougars finished 4-8 this season, the best record of his tenure.
Moos said Tuesday he was looking for a coach who would lead a high-powered offense that would win games, fill the stands at Martin Stadium and prompt donors to open their checkbooks. Leach would seem to fill all those criteria.
Construction has already started on an $80 million project to add premium seating, luxury boxes and a new press box. Also on the drawing board is a $60 million football operations building.
“I asked Athletic Director Bill Moos to select the best head football coach in the country and I am convinced that he has done exactly that,” WSU President Elson S. Floyd said in a statement.
Leach was born in Susanville, Calif., and raised in Cody, Wyo.
At Texas Tech, his offense led the nation in passing six times and three times accumulated the most total yards. In 2009, the Red Raiders were second in passing offense and fourth in total offense, with both marks tops among BCS conference schools.
Defensively, Texas Tech held opponents without an offensive touchdown a dozen times under Leach, including seven shutouts.
Leach spent one season as the offensive coordinator at Oklahoma (1999), as the Sooners set six Big 12 Conference records. He spent two seasons in a similar capacity at Kentucky (1997-98), the only two seasons in school history in which it passed for more than 4,000 yards.