The Robert Griffin-led Bears (9-3, 6-3 Big 12) finished the season with five straight wins for their longest streak since 1991. The Bears' nine wins are their most since 1986.
Washington (7-5, 5-4 Pac 12) is in a bowl for the second straight year under third-year coach Steve Sarkisian.
The game could be Griffin's last as a collegian. He's projected as a high pick if he decides to enter the NFL draft.
A fourth-year junior who has graduated, Griffin said Sunday he would probably wait until around the Jan. 17 deadline for underclassmen to make a decision on whether to go pro or stay in school.
He'll find out Monday if he's invited to New York as a Heisman Trophy finalist. College football's outstanding player will be named Saturday.
"It would be cool," Griffin said of a possible invitation. "I'm not saying if they say, `Hey, do you want to come?' I'd say, `No.' Please extend the invitation and I'll go."
Baylor and Washington will be playing for the fifth time but first since 1965. The Bears have won three of the four previous meetings.
The Alamo had the first choice of Pac-12 teams that didn't receive BCS bids. The Alamo chose Washington over California. The Golden Bears were also 7-5 but finished a game behind the Huskies and Utah in the Pac-12 North.
Baylor received the Alamo bid after the Cotton Bowl selected Kansas State.
Last year, the Huskies beat Nebraska 19-7 in the Holiday Bowl.
"We're excited to play in the Valero Alamo Bowl and to represent the University of Washington and the Pac-12 Conference," Sarkisian said in a statement. "The selection is a testament to the hard work our team has put in, and we look forward to a great trip and exciting game."
The Huskies have a pretty good quarterback, too, in Keith Price, who set a school record with 29 touchdown passes.
Baylor goes into the postseason with a different mentality this season. Last year, the Bears lost three straight to end the regular season and were beaten 38-14 by Illinois in the Texas Bowl.
"We were coming off three tough losses and we were excited about being in a bowl game because it was the first time in 16 years," Bears coach Art Briles said. "We're coming off of five victories where it's not `Who's next? What's going to happen?' We have a real good idea how we're going to perform. So that is very comforting going into this bowl as opposed to a year ago."
Griffin, one of three players in major-college football history with 10,000 yards passing and 2,000 yards rushing, said he and his teammates are brimming with confidence after beating Texas on Saturday.
"Offense is putting up a lot of points and a lot of yards," Griffin said. "If anybody is going to play us right now, it's going to be a tough matchup. If we go out and be us, then no one can beat us."