Sarkisian in 2009 took over a Washington program that went 0-12 the previous season, and he returned the Huskies to respectability. He led Washington to a 34-29 record (24-21 Pac-12) in five seasons.
The Huskies (8-4) finished third in the Pac-12 North with a 5-4 conference record. They had three straight seven-win seasons entering this year.
Sarkisian thanked Washington and said he believes he left the program in a better place than when he started.
"I am extremely excited to be coming home to USC and for the opportunity that USC presents to win championships," he said in a statement. "I can't wait to get started."
Orgeron resigned Monday after he was passed over for the job, a source said.
Orgeron was "outraged" by athletic director Pat Haden's decision, even though Haden offered to make Orgeron an assistant head coach and one of the nation's highest paid assistants, according to the source.
The Trojans went 6-2 under Orgeron after Haden fired Lane Kiffin on Sept. 28.
USC's statement said Orgeron will pursue other head coach openings.
"I am grateful to the University of Southern California for the great time I had here," Orgeron said in the statement. "I'm especially grateful for the players on this year's team, the coaching staff and the Trojan Family for the way they all fought through adversity and became one. I'm also thankful for all the Trojan players and family members who have become close personal friends during my 11 years at USC. I am especially proud of this year's team and coaching staff, who had to start a new season and then bonded, played together as a family and competed like Trojans. I'll forever be grateful to the University of Southern California. Fight On!"
Sarkisian, 39, interviewed with USC over the weekend, a source said. Boise State's Chris Petersen was a top candidate but withdrew from consideration, according to the source. Vanderbilt's James Franklin was also a candidate for the job, the source said.
USC will host a news conference Tuesday afternoon to introduce Sarkisian.
Sarkisian, a native of Torrance, Calif., who played at El Camino Junior College, was an assistant at USC for seven seasons (2001 to 2003 and 2005 to 2008). He also played baseball at USC before transferring.
"We are delighted to welcome Steve Sarkisian back to the Trojan Family," Haden said in a statement. "We conducted a very exhaustive and thorough search, pinpointing about 20 candidates and interviewing five of them. We kept coming back to Sark. He is the only one who was offered the job. I believe in my gut that he is the right coach for USC at this time."
In 2007 and 2008, he was the Trojans' assistant head coach and offensive coordinator. When Sarkisian was on USC's staff under coach Pete Carroll, the Trojans were 74-15 -- including 22-3 when he was offensive coordinator.