Both sources say Arkansas will officially announce the hiring Tuesday.
Bielema, fresh off leading the Badgers to a third consecutive Rose Bowl appearance with their victory over Nebraska this past Saturday, leaves Madison with a career record of 68-24.
He replaced long-time Wisconsin coach Barry Alvarez in 2006, who now serves as the athletic director for the school.
Wisconsin has not announced whether Bielema will coach in January's Rose Bowl game against Stanford.
Arkansas expected to be looking for a coach this off-season after hiring John L. Smith on just a 10-month contract. Smith was brought in to replace Bobby Petrino, who was fired during a scandal where he hired his mistress to work in the football department.
Arkansas went 4-8 this season under Smith, after going 21-5 the previous two seasons with Petrino as coach. Bielema will certainly be expected to return the football program back to an SEC conference power.