The two-time all-star goaltender signed a six-year contract worth a total of US$39 million with Montreal on Monday.
Price, who turns 25 on August 15, already has five NHL seasons under his belt.
"It kind of made sense to me," Price said on a conference call from Williams Lake, B.C. "It will take me to until I'm 30 years old and generally that's about the peak of goaltenders, so I'm hoping by then to have a couple of Stanley Cups and have a good re-negotiation when I'm 30."
Canadiens fans would dearly love to conjure up hope of winning one more Stanley Cup after the team finished 15th — dead last — in the Eastern Conference. Montreal has not won a Cup since claiming its record 24th title in 1993.
With that goal in mind, Price is ready to assume still higher expectations from the team's demanding fans.
"There's a tremendous amount of pressure on us no matter what you're making, so it might make you a target a little more," he said." But being a goaltender, I'm used to that anyway."
Montreal general manager Marc Bergevin announced the signing.
"I think Carey brings what we need moving forward," Bergevin said. "He's a top goalie in the league, a young goalie, and with having him in the net for the next six years I think it gives our team a chance to be competitive, and moving forward I think it was a key for us to have Carey in Montreal."
Bergevin, who was hired on May 2, added three free agents to the Canadiens' roster Sunday.
"It's been a pretty interesting summer to watch, not only the changes that have been going on up top but also the players that we have signed recently," Price said.
Brandon Prust left the New York Rangers to sign a four-year, $10 million contract with Montreal. Colby Armstrong signed a one-year deal for $1 million and veteran defenceman Francis Bouillon agreed to a one-year contract worth $1.5 million.
"I just like these guys," Bergevin said. "They bring character, they bring sandpaper, they bring personality to our club which I feel was missing last year. From day one I wanted to build this team around character guys that put the team first, and that's what I think we did.
Price played 65 games for the Canadiens last season. He posted a 26-28-11 record with a 2.43 goals-against average, a .916 save percentage and four shutouts.
Drafted by Montreal in the first round, fifth overall, of the 2005 NHL draft, the native of Anahim Lake, B.C., has a 124-104-35 record with 16 shutouts, a 2.56 GAA and a .916 save percentage.
He is already eighth on the Canadiens' career list for both wins and games played by a goalie (271).
"It's huge for me," Price said. "Obviously it's an honour to come back and to have the vote of confidence from the organization of my hockey club is huge as well. It's nice to see that they show a lot of confidence in me and now I have to go out there and prove them right."