Bielema's surprise move came only three days after he led the Badgers into their third straight Rose Bowl with a 70-31 shellacking of Nebraska in the Big Ten championship game.
"Coach Bielema has led his team to a historic run of championships while seeing a record number of student-athletes recognized for academic achievement," Arkansas Athletics Director Jeff Long said.
"His tough, aggressive style of play has been successful and will be appealing to student-athletes and Razorback fans."
Bielema, 42, racked up a 68-24 record in seven seasons at Wisconsin, compiling an 8-5 mark this year.
He replaces John L. Smith, who was let go in the wake of a 4-8 season after taking over in April for the fired Bobby Petrino.
It remained unclear if Bielema would be on the sidelines during the Jan. 1 Rose Bowl, in which Wisconsin will take on Pac-12 champion Stanford.