Sarkisian has never been a head coach at any level of football.
The Huskies have an 0-11 record this season and dismissed Tyrone Willingham as their head coach.
Sarkisian, 34, has been an assistant head coach and quarterbacks coach for USC since 2005. He had served a previous tenure with the Trojans before taking the job as quarterbacks coach for the Oakland Raiders in 2004.
Sarkisian played college football with Brigham Young. He led the Cougars to a 13-1 record and the WAC title in 1996, and then played three seasons in the Canadian Football League with the Saskatchewan Roughriders.
Washington interviewed Texas Tech Coach Mike Leach, Fresno State Coach Pat Hill and Cincinnati Coach Brian Kelly for the job.
The Huskies have a game remaining this season at California and Willingham will coach the team for that contest.