The 33-year-old Norwegian, who was released by Rovers after his conract expired at the end of last season, has signed a one-year deal at Ibrox.
“We are delighted to have reached agreement with Henning Berg and I know Alex is looking forward to working with him," Rangers Director of Football, Martin Bain told the Rangers official website.
“The medical went smoothly and all the paperwork was completed and now Henning is just desperate to get going in his new surroundings.”