He replaces John Anderson, who didn't return after two years with the Coyotes.
The 51-year-old Brown spent the past three seasons with Vancouver, working on a staff that helped lead the Canucks to the Presidents' Trophy in consecutive seasons and a trip to the 2011 Stanley Cup finals.
Brown also has served as an assistant coach for Anaheim, Columbus and Chicago in an NHL career that dates to the 1996-97 season. He also was the head coach for four seasons with Adirondack, the Detroit Red Wings' AHL affiliate.
It's a date that's been circled on my calendar, so it's kind of nice to have it here and get it over with (Thursday). This is a little bit of the closing of the book on the move. That's kind of how I'm looking at it.
— Stars forward Jason Spezza on returning to Ottawa for the first time to face the Senators