Gudbranson has four points (two goals, two assists) in 41 games this season, and 53 points (14 goals, 39 assists) in 380 NHL games with the Florida Panthers and Canucks.
"I can only get better," Gudbranson said. "There's a lot of work to be done. I'm still a sponge like I was when I was 19, 20 years old, trying to pick guys' brains and use the vets to my advantage.
"I don't know what the ceiling is, I don't think anybody really knows. I'm just trying to get better every single day and that's my motivation to be here. Any hockey player's motivation is to constantly get better."
Green has been using the pair of Gudbranson and Alexander Edler in a shutdown role; it's a move that Gudbranson said helped him decide to stay.
"I think the last two months I have started to feel really comfortable," he said. "The pairing I am part of right now gives me a little more purpose on the back end. Stuff like that gets me going. It excites me making guys' nights miserable. I have been able to do that and I felt comfortable out there. That certainly gave me a positive mindset going into the negotiations."
The No. 3 pick in the 2010 NHL Draft was acquired by the Canucks in a trade with the Panthers for center Jared McCann on May 25, 2016.
"Erik is an important part of our team and provides a physical element to our blue line," Canucks general manager Jim Benning said. "His leadership qualities help us as we continue to integrate younger players in our lineup. He is a quality person, a great teammate, outstanding in the community and we are excited to have him as part of our team moving forward."
The Canucks (23-30-6) play the Colorado Avalanche at Rogers Arena on Tuesday (10 p.m. ET; SNP, ALT, NHL.TV). Vancouver is 19 points out of a Stanley Cup Playoff position in the Western Conference.
