The center was eligible to become an unrestricted free agent on July 1.
Plekanec led Montreal last season with 70 points, including 25 goals. He added four goals and seven assists in 19 postseason games to help the Canadiens make a surprising run to the Eastern Conference finals. His regular season was a big improvement from 2008-09 when he had 20 goals and 39 points.
"I knew I had a bad year the previous year and I wanted to start strong, and I had a good start," Plekanec said from his home in Kladno, Czech Republic. "I knew I had to get stronger mentally and that's what happened."
Plekanec and Mike Cammalleri clicked on a line with winger Andrei Kostitsyn. He had played with Kostitsyn and former teammate Alex Kovalev before that.
"I wanted to prove that I could do it without Kovy," he said. "Obviously playing with Cammalleri, and with Andrei for some of the games, was helpful for me and the team."
Plekanec is also a strong defensive player who is adept at taking faceoffs.
"I'm asked to play a two-way game and I do it," he said. "My job is the same in the playoffs — to play a two-way game and help the team win, not (just) score goals. I will do the same for another six years."
In 393 career NHL regular-season games, the Czech Olympian has 103 goals and 151 assists.
Plekanec was drafted in the third round by the Canadiens in 2001.
"I've been part of the organization for eight years and I have a chance to be part of it for another six years, so I know what's it all about and I love everything about it," he said. "There was no question of wanting to leave."
Earlier Tuesday, the Canadiens signed fourth-line winger Mathieu Darche to a one-year contract worth $500,000.