Willie Desjardins was fired as coach April 10.
Green, 46, has coached Utica, the Canucks' American Hockey League affiliate, for the past four seasons; he is 155-110-27-12 in 304 games. Utica reached the Calder Cup Playoffs twice, including the final in 2015, where it lost to Manchester, the Los Angeles Kings' affiliate, in five games.
Utica finished fifth in the North Division with 79 points (35-32-7-2) this season, three behind St. John's for fourth place and the final playoff berth in the division.
Prior to joining the Vancouver organization, Green spent three seasons with Portland of the Western Hockey League. The Winterhawks won the WHL championship in 2012-13, when Green was coach and general manager.
Green played 14 NHL seasons with the New York Islanders, Mighty Ducks of Anaheim, Phoenix Coyotes, Toronto Maple Leafs and Boston Bruins. He had 455 points (193 goals, 262 assists) in 970 games.
