The Stars (42-32-8, 92 points) finished 10th in the Western Conference last season and missed the playoffs for the second straight season. Montgomery, who was hired on May 4, is the third Stars coach in three seasons.
Having played for Lindy Ruff in 2016-17 and Ken Hitchcock in 2017-18, Klingberg welcomed Montgomery's efforts to make the transition as easy as possible.
"He's young in terms of coming into the League," Klingberg said. "First timer. But I think that can be a good thing as well because you kind of have to take that step that you need to have that communication to build that off. I think that that's something he's already proved by coming over to Sweden and having lunch with me."
Montgomery, 49, spent the past five seasons at the University of Denver, where he had a 125-57-26 record and coached the team to the NCAA title in 2017.