They have played four times, but never in a bowl game.
The match-up, announced Sunday, marks USC's first Holiday Bowl appearance. Kick-off is at 5 p.m., and the game will be televised by ESPN.
First-year USC Coach Steve Sarkisian led Washington to a victory over Nebraska in the 2010 Holiday Bowl.
"We are excited to go play in the Holiday Bowl and be the first USC team to do so," Sarkisian said in a statement. "We get to play close to home, and our fans will show up in force."
USC, No. 24 in the final College Football Playoff ranking released Sunday, was also thought to be under consideration for a spot in the Alamo Bowl in San Antonio, Texas. But Alamo Bowl organizers chose No.14 UCLA to play No. 11 Kansas State.
The Holiday Bowl has longed for the Trojans.
"These are two traditional powerhouse programs that will draw die-hard fans as well as the casual college football fan," Holiday Bowl President Vincent Mudd said in a statement. "We can't wait to welcome these teams and their outstanding fan bases to our city."
USC finished the regular season with an 8-4 record. The Trojans enter the bowl game with momentum after their 49-14 rout of Notre Dame on Nov. 29.
Nebraska, of the Big Ten Conference, is 9-3. Former Oregon State Coach Mike Riley was hired last week by Nebraska to replace Bo Pelini, who was fired two days after the Cornhuskers' season-ending 37-34 overtime victory over Iowa.
Cornhuskers assistant Barney Cotton is interim coach for the bowl game.
Last season, Nebraska defeated Georgia in the Gator Bowl.
"We would like nothing more than to send our seniors out with a second straight bowl victory and a 10-win season," Cotton said in a statement.
Nebraska is 1-2 in the Holiday Bowl, including a 19-7 loss to Sarkisian's Washington team in 2010.
USC is 3-0-1 against Nebraska. In 2007, the Trojans defeated the Cornhuskers, 49-31, at Lincoln, Neb.
USC defensive coordinator Justin Wilcox said after Sunday's morning practice that he had not been contacted about head coaching positions.
Wilcox has been mentioned in media reports as a possible candidate to replace Riley at Oregon State.
"People think that everybody's talking to a lot of people — it's not like that," said Wilcox, who reportedly interviewed to replace Chris Petersen at Boise State after the 2013 season. "We're recruiting, self-scouting and getting ready for the bowl game."
Wilcox said it was not difficult to remain focused when coaches' names are linked to openings or interest from other programs.
"I learned this a long time ago — especially in our profession — if you worry about those things, you're missing the boat," he said. "We need to worry about what we need to do to play better…. That's what you concern your time with, and that's all that matters."
Asked whether he would like to become a head coach, Wilcox said, "I want to do the best possible job I can do to help our team win. That's all I care about…. Some people are 10 years down the road. I don't operate like that."
Tickets to the Holiday Bowl range from $65 to $140, the Holiday Bowl's website said…. Receiver JuJu Smith, who was sidelined Saturday because of an ankle sprain, returned to practice…. Sarkisian said cornerback Rahshead Johnson, offensive lineman Chris Brown and linebacker Malik Dorton — all freshmen — were players who made strides during the last three practices.