"Tim helped implement a winning culture in Reading that ultimately led to a championship," Bruder said. "He is ... a bright young coach with high energy. We are very excited to have him in Utah."
Branham is a native of Eagle River, Wis. He was a third-round pick by Vancouver in the 2000 NHL entry draft. During an eight-year professional career, he played 284 games in the ECHL and the American Hockey League.
The Grizzlies will formally introduce Branham as their coach in August, after he relocates his family to Utah.
In a statement issued by the team, Branham thanked Grizzlies owner Dave Elmore and Bruder for giving him his first head coaching opportunity.
"This is a first-class organization with top-notch facilities," Branham said. "My wife and I are thrilled to move to Salt Lake City and join the Utah Grizzlies family. I look forward to building an exciting team for the fans."
The Royals posted a record of 143-89-23 and won seven playoff series during Branham's four years in Reading. They were 16-6 in the playoffs this season.
Branham becomes the seventh coach in Grizzlies history. He replaces Kevin Colley, who resigned two weeks ago to accept the coaching job with the Prescott Valley-based Arizona Sun Dogs of the Central Hockey League.