With the team stuck in last place in the Pacific Division, Bruce Boudreau was hired to replace Green. Boudreau is the Canucks' 20th coach.
Also fired were assistant GM John Weisbrod and assistant coach Nolan Baumgartner.
"First, I want to sincerely thank Jim, John, Travis and Nolan for their passion and dedication to the organization and our community," Canucks chairman Francesco Aquilini said in a statement. "We are grateful for everything they have done for the Canucks during their tenure, and we wish them nothing but success in the future.
"These are difficult decisions, but we believed we would have a competitive group this year. As a result, I'm extremely disappointed in how the team has performed so far. I'm making these changes because we want to build a team that competes for championships and it's time for new leadership to help take us there."
Scott Walker, 49, was named assistant coach to Boudreau. Walker spent four seasons playing right wing for the Canucks from 1994 to '98. He previously coached the Ontario Hockey League's Guelph Storm and worked as the Storm's president of hockey operations.
Stan Smyl will serve as Vancouver's interim GM, with Ryan Johnson taking on the role of interim assistant GM.
The shake-up come a day after a disheartening home loss in which fans voiced their displeasure with "Fire Benning" chants. The 58-year-old Benning was known for some solid draft picks and questionable free-agent signings over his eight seasons as GM.
Green was promoted to Vancouver's bench on April 26, 2017, after coaching the club's American Hockey League affiliate, the Utica Comets. Despite an impressive run in the NHL playoff bubble of 2020, he was dismissed after 289 games, finishing with a 125-132-32 record.
Vancouver made the postseason only once in Green's tenure, during the pandemic-shortened 2019-20 season, but that run was promising. The Canucks advanced to the second round in Edmonton, Alberta, that summer, eventually falling to the Vegas Golden Knights.
This season has been abysmal for Vancouver, with the Canucks owning the second-worst record in the Western Conference at 8-15-2.
Last month, Green deflected questions about being on the hot seat amid the growing chorus of disgruntled fans calling for change.
"I don't listen to the noise," Green told reporters. "I only worry about coaching the team. I do understand when people get upset. But ... it doesn't have an effect on me one way or the other."
Shortly after Green made those comments, Benning met with the media, and he didn't give Green a vote of confidence.
"We're looking at everything," Benning said at the time. "We're trying to find solutions to our problems, and Travis and his staff are working hard. Losing is wearing on them, like it's wearing on all of us. This is something that I didn't expect to happen after the moves we made this summer. But it's happening, and we have to deal with it."
After a spring of headlines around his future, Green reached an agreement on a contract extension with the Canucks on May 21, adding two more years to his deal. But there have been several issues for the Canucks this season, the most glaring of which is their lack of star power, and Green just wasn't able to find the right mix.
Star center Elias Pettersson, who signed a three-year, $22 million contract in October, has been nearly invisible, with just four goals in his first 25 games. Brock Boeser led Vancouver in points last season, but he has just 10 points in 22 games thus far. Even captain Bo Horvat has struggled, producing just 13 points.
By late November, not even Canucks players were hiding their frustrations any longer. After a 4-1 loss to the Pittsburgh Penguins, marking Vancouver's seventh defeat in eight games, J.T. Miller was asked if everyone in the dressing room was still buying in.
"I don't know," Miller said, sparking another tidal wave of criticism levied against the Canucks' underperformance.
Coincidentally, it was another 4-1 loss to the Penguins -- Saturday on home ice -- that seems to have been the final nail in Green's coffin. As such, the pressure to turn things around quickly under Boudreau and the new staff will be intense.
This opportunity with the Canucks will be Boudreau's fourth stop as an NHL coach, after stints with the Washington Capitals, Anaheim Ducks and Minnesota Wild. He was working as an analyst for the NHL Network this season.
Boudreau was fired by the Wild in February 2020, after a 27-23-7 start to the 2019-20 season. In all, Boudreau has coached 984 NHL games, with a 567-302-115 record.
Boudreau will be behind the bench Monday night, when Vancouver plays host to the Los Angeles Kings.
The Associated Press contributed to this report.