The deal has an average annual value of $5.5 million.
The 26-year-old Kuzmenko has played in 47 games for the Canucks this season with 21 goals and 22 assists, four penalty minutes and a plus-4 defensive ranking.
Kuzmenko ranks second on the team in goals and power-play goals (nine). His 43 points are tied for third, while his 32 even-strength points (12 goals, 20 assists) rank second. He leads all Vancouver skaters in shooting rate (24.7%) and ranks third in the NHL in that category (minimum 20 games).
He leads all first-year NHL players in almost every offensive category, including goals, assists, points, points per game (0.91), power-play goals and power-play points.
Kuzmenko has had 14 multipoint games this season (second on the Canucks), highlighted by his first career hat trick and season-high four-point game against the Anaheim Ducks on Nov. 3.
A native of Yakutsk, Russia, Kuzmenko spent his first eight professional seasons in the Kontinental Hockey League with CSKA Moscow and SKA St. Petersburg, getting 200 points (85 goals, 115 assists) in 315 regular-season games. He set career highs in goals (20), assists (33) and points (53) last season, ranking second in the league in scoring.
Kuzmenko has represented his country on the international stage on multiple occasions, totaling 16 points (10 goals, 6 assists) and six penalty minutes in 37 games.
He was originally signed by Vancouver to a one-year, entry-level contract on July 13.