Tanguay was an assistant coach the last two years for the Iowa Wild in the American Hockey League. He had 863 points during a 16-year NHL career, which included two stints with the Colorado Avalanche.
Yzerman in May gave coach Jeff Blashil l a contract extension despite a five-year postseason drought and 172-221-62 career record.
The Red Wings are in the midst of a franchise rebuild, and found the makeshift Central Division a struggle this season. The Central had three teams with 75 or more points, including the Tampa Bay Lightning, who are leading the Stanley Cup Final. Detroit finished tied for last with the Columbus Blue Jackets, both with 48 points.
Tanguay, 41, played in the NHL for 16 seasons, and was a key contributor in Colorado at the pinnacle of the Red Wings-Avalanche rivalry in the 1990s.
The Associated Press contributed to this report.