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 cool when you think about how many great American players have played the game and the two players that were at that 18-game point streak and what they've done in their careers. It's pretty cool right now, but it was kind of overshadowed by the loss.
— Blackhawks forward Patrick Kane after breaking the record for longest point streak by an American-born player with a goal and an assist in a 3-2 overtime loss against the Kings