The 26-year-old forward, who is a free agent after playing eight seasons in the Kontinental Hockey League, is eligible to sign on July 13.
"I have been watching Andrei since his 2014-15 season and have been impressed with his development and improvement on the ice," Canucks general manager Patrik Allvin said. "Once the contract details are finalized, we look forward to welcoming him to the Canucks organization and helping him continue to grow as a hockey player."
Kuzmenko is coming off his best season in the KHL, finishing second in the league with 53 points (20 goals, 33 assists) in 45 games for St. Petersburg. He led SKA in points and assists and was second in goals.
"We would like to thank all the teams that we met with for their time and interest," Kuzmenko's agent Dan Milstein said. "We were impressed by what the Canucks organization wants to accomplish and the winning culture they are building. Andrei felt a good connection with the management team and is looking forward to playing for (coach) Bruce Boudreau."
Although Vancouver (40-30-12) missed the Stanley Cup Playoffs for the sixth time in seven seasons, it finished 32-15-10 under Boudreau, who replaced Travis Green on Dec. 5. The Canucks announced on May 13 that Boudreau would return as coach.
