Andersen, the Badgers' coach for two seasons, informed the team of his decision Wednesday afternoon, the school said.
Andersen replaces Mike Riley, who left the Pac-12's Beavers to accept the head coaching job at Nebraska after the dismissal of Bo Pelini. Oregon State finished this season 5-7 and had two conference wins, but one came at home against then-No. 7 Arizona State.
Andersen thanked Wisconsin in a prepared statement.
"We worked very hard together and accomplished some great things. I had the opportunity to meet and coach some great young men and I look forward to watching them as they continue their careers and move through life," he said.
The Badgers had an inconsistent season, losing two of their first five games but recovering to win seven straight. But the season ended with a thud when the team was blown out by Ohio State 59-0 in the Big Ten championship game.
Azusa Pacific running back Terrell Watson headlines this season's American Football Coaches Assn. Division II Coaches' All-America team.
Watson was the leading rusher in Division II this season with 2,153 yards in 319 carries. He scored 29 rushing touchdowns, which also leads the nation. Watson's 195.7 yards per game also led all Division II players.
Other Southern California players named to the coaches' All-America team are offensive lineman Mike Lorenzo, of Chadron State (Nebraska), who played at Westlake Village Westlake High, and Humboldt State defensive lineman Alex Markarian, who played at Ayala High in Chino Hills.