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.
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.
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.
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).
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.
Leinart on Monday praised the hire on Twitter.
I think Sark is a great hire. I was with him for 4 of my 5 years at USC. Great recruiter, motivator and teacher! Really happy for him #sc— Matt Leinart (@MattLeinartQB) December 2, 2013
USC freshman tailback Justin Davis also wrote on his Twitter account that he approved the decision to hire Sarkisian.
I'm on board Sark was very close to getting me to come with him to U Dub— Justin Davis (@JD_22bsm) December 2, 2013
Washington freshman quarterback Troy Williams, a Los Angeles native, expressed his displeasure with the move, writing: "Don't ever commit cus of a coach. Faker then a 3 dollar bill." The tweet was later deleted.
After going 5-7 in his first season, Sarkisian took the Huskies to a bowl game each of the next four seasons, but they were stuck on seven wins for three years. The Huskies finished this regular season 8-4, with a victory over Washington State in last Friday's Apple Cup.
Sarkisian said after Friday's victory that he was thankful he no longer had to answer questions about the seven-win barrier.
"We're a better team today that we were a year ago, and a year ago we were a better team than a year before that," Sarkisian said. "Sometimes games go the way they go and you don't get the call or you don't get the catch or you make the one bad call as a coach. But that doesn't mean you're not a good football team or you aren't a better team than you were a year before."
Sarkisian was in the middle of a contract that runs through 2015 and paid him about $2.25 million per year before jumping to $2.85 million in the final season.
Sarkisian never beat Oregon in his tenure, an issue that stuck with Washington fans tired of getting beaten up by their neighbors to the south.
Sarkisian is the first Washington coach to voluntarily leave for another position since Darrell Royal in 1956 when he departed for Texas. Royal was at Washington for one season.
USC offensive coordinator Clay Helton is expected to be the interim coach in the Trojans' bowl game, a source said.
Information from ESPN's Joe Schad and Brett McMurphy and The Associated Press was used in this report.