The 42-year-old Frost takes over for Mike Riley and is tasked with rebuilding the football program.
The Cornhuskers finished the season 4-8 after a 56-14 loss at home to Iowa on Friday.
Martin Krampelj had career highs in his first career start.
Shawn Eichorst was let go four weeks ago after the Cornhuskers lost to Northern Illinois at home.
Adidas has been Nebraska's apparel sponsor since 1995.