A news conference is scheduled for later in the day.
"We believe in Trevor's leadership abilities," Canucks owner Francesco Aquilini said in a statement. "His 20 years of NHL experience including seven as team captain, his role as NHLPA President, community leader and businessman offers a very special skill set; one that will positively shape the direction of this club in the future.”
The Canucks said Linden, who turns 44 this year, will be in charge of all aspects of hockey operations.
"I’m passionate about the Canucks and I want to win – just like our fans. I believe in this team and share the organization’s commitment to excellence on and off of the ice," Linden said in the statement. "I am looking forward to getting started – getting to know everyone in the organization, and working together to win the Stanley Cup for this great city and Province."
Selected second overall in the 1988 NHL draft, Linden holds the franchise marks in games played (1,140) and assists (415) and second in goals (318) and points (733) in franchise history.
Overall, he scored scored 375 goals and added 492 assists for 867 points in 1,382 career NHL games, with stops also in Washington and Montreal.
He has stayed active in Vancouver since retiring, including running a chain of health clubs.
Gillis was fired on Tuesday after six years at the helm, and just three seasons removed of a Stanley Cup Final appearance for the Canucks. But Vancouver on Monday was officially eliminated from the playoffs for the first time in six seasons.
Linden will determine who will coach the Canucks next season, either John Tortorella or a name yet to be determined.