The announcement came just hours after Hill announced John Van Dam as the team's offensive coordinator.
Paulson was most recently the assistant coach and defensive backs coach at Northern State University in South Dakota, where he was hired April 28.
Prior to Northern State, he served as the assistant head coach, defensive coordinator and linebackers coach at University of Nevada, Las Vegas. In 2014, he was part of the Rebels team that appeared in the Football Bowl Subdivision Heart of Dallas Bowl, which the team lost to North Texas 36-14.
Paulson had two stints at Montana that spanned more than 15 seasons.