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.
Once again, it shows character in this dressing room. Once again, there's no quitting in here. We all wanted this so bad and we worked so hard to get home-ice advantage and we weren't going to let this one slide.
— Colorado Avalanche captain Gabriel Landeskog on his team's OT Game 1 win vs. Minnesota Wild