Bieksa, 30, a pending free agent, posted 22 points and was a plus-32 in 66 regular-season games for the Canucks, adding 10 points in 25 playoff games that saw Vancouver come within one win of a Stanley Cup title.
His big moment in the playoffs came when he scored a flukey goal on a carom off a stanchion in double-overtime that lifted the Canucks past San Jose and into the Stanley Cup Finals.
The Canucks will take a salary cap hit of $4.6 million with the deal, The Vancouver Sun reported.
The team didn't confirm Bieksa's signing.
Three other Vancouver defensemen remain unsigned heading into the July 1 free agency period, including 50-point scorer Christian Ehrhoff, veteran Sami Salo and bench player Andrew Alberts.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys