Sarkisian, who compiled a 34-29 record in five seasons with the Huskies, replaces interim Coach Ed Orgeron, who took over from the fired Lane Kiffin in late September.
USC Athletic Director Pat Haden said Orgeron had left the program to pursue a head coaching job elsewhere.
The Trojans went 6-2 under Orgeron -- including five consecutive victories and an upset of No. 5 Stanford -- but finished the season with a 35-21 defeat at the hands of UCLA.
Sarkisian, 39, was a top assistant under Pete Carroll at USC before going to Washington.
"He embodies many of the qualities for which we looked," Haden said. "He is an innovative coach who recruits well and develops players. He is a proven and successful leader. He connects with people. He has energy and passion."
"I am extremely excited to be coming home to USC and for the opportunity that USC presents to win championships," Sarkisian said. "I can't wait to get started."