The school will have a press conference at 2 p.m. (et) Monday to make the announcement.
Willingham spent the past three seasons at Notre Dame, where he compiled a 21-15 record. He was 44-36-1 in seven previous seasons at Stanford. Willingham was the Pac-10 coach of the year in 1995 and 1999 and the National Coach of the Year in 2002.
Willingham replaces Keith Gilbertson, who stepped down at the end of the 2004 season. Willingham becomes the third Washington coach in just four years, as Gilbertson had taken over after the Rick Neuheisel scandal.
The Huskies suffered through the worst campaign in school history at 1-10 this past season, including 0-8 in the Pac-10, and finished with just a 7-16 mark in Gilbertson's two years at the helm.
Willingham was fired by Notre Dame after going 6-5 this past season.