Rutherford also will be general manager while he leads the search for someone to fill that role.
"It is an honor to join the Vancouver Canucks and to lead an NHL team in Canada," Rutherford said. "I would like to thank [owner] Francesco [Aquilini] and the Aquilini family for the opportunity. The Canucks have an exciting young group of players, and I look forward to building a plan that will take this team to the next level and excite Canucks fans everywhere."
A three-time Stanley Cup champion and a Hockey Hall of Famer, Rutherford resigned as general manager of the Pittsburgh Penguins on Jan. 27 because of personal reasons but didn't rule out working in the NHL again.
"The timing was good for me to totally have a reset and get away from the pressure and just view the game a little bit different, and really enjoy every game," Rutherford told Sirius XM NHL Radio on Nov. 29. "I certainly have enjoyed the games and I watch every night, follow every team and stay abreast of what's going on. So at some point in time, I may get back in."
The Canucks fired coach Travis Green and general manager Jim Benning on Sunday after a 9-15-2 start. Green, who was in his fifth season as coach, was replaced by Bruce Boudreau. Benning, in his eighth season as general manager, was replaced by Stan Smyl.
Vancouver is 2-0-0 since Boudreau became coach.
"It is time for a new vision and a new leader who will set a path forward for this team," Aquilini said. "Jim has tremendous experience building and leading winning organizations and I believe he will help build the Vancouver Canucks into a team that can compete for championships again."
With Rutherford as GM, the Penguins won the Stanley Cup in 2016 and 2017; they were the first team since the NHL instituted a salary cap in 2005 to win back-to-back championships. He was voted the General Manager of the Year Award winner for the 2015-16 season and in 2019 was inducted into the Hockey Hall of Fame as a Builder.
Prior to his seven seasons with the Penguins, Rutherford worked 20 seasons as GM and president of the Hartford Whalers/Carolina Hurricanes (1994-2014). The Hurricanes won the Stanley Cup in 2006.
"I've known Jim for 45 years," Boudreau said Friday. "We were teammates in Toronto (with the Maple Leafs in 1980-81). I keep reminding him I scored my first goal against him and then he got traded a week later, so I got him booted to the Leafs. When you talk about Jim, it's respect for what he's done in this league, winning three Stanley Cups, and just retooling teams time after time, and the respect he holds from the rest of the people in the league and being a Hall of Fame guy, I mean, I don't think this team could have done any better in getting somebody to overlook the next wave of Canucks."
NHL.com independent correspondent Kevin Woodley contributed to this report