The Razorbacks announced Ash's hiring on Tuesday, Bielema's first of an assistant coach since being hired last week at Arkansas after seven seasons at Wisconsin.
Ash worked under Bielema with the Badgers for the past three seasons, including the last two as co-defensive coordinator. He'll remain with the team through its Rose Bowl appearance against Stanford.
"I am excited to welcome Chris to our staff," Bielema said in a statement. "In the last three years working together, I gained a great respect for the way Chris teaches the game and develops student-athletes. I've followed his career for a long time, and his knowledge of the way we run our program and specifically the defense will be valuable for us moving forward in our transition."
Ash came to Wisconsin from Iowa State, taking over as the Badgers' defensive backs coach in 2010. The Badgers allowed just 193.9 yards passing per game that season, and three of their secondary starters earned All-Big Ten honors.
The 38-year-old was elevated to defensive coordinator in 2011, and helped lead a Wisconsin defense that was 13th in the country -- allowing 19 points per game.
The Iowa native began his coaching career at Drake, and he's also worked at San Diego State. He served as Drake's defensive coordinator for two seasons before joining the Iowa State staff in 2000. He spent eight of the next 10 seasons with the Cyclones, working primarily with the defensive backs and also as the school's recruiting coordinator.
This season, Wisconsin has allowed 320.9 yards per game and ranks 13th in the country in total defense -- 24th in passing defense.
Ash will take over an Arkansas defense that struggled mightily in its first season after the firing of Bobby Petrino. The Razorbacks were 113th in passing defense, allowing 285.8 yards per game, and were 12th in the 14-team Southeastern Conference -- allowing 30.4 points per game.