Financial terms were not released.
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The 28-year-old forward tied his NHL career high with 24 points (nine goals, 15 assists) in 69 games with the Columbus Blue Jackets last season and had four points (three goals, one assist) in six Stanley Cup Playoff games.
"I think I was looking for somewhere where the team was solid, the team was growing," Calvert told the Avalanche website. "It's a very young team, they got some very good players, I think that was a first priority. I want to win, and I really can see us doing that in Colorado. …
"You get a small pick of maybe a couple teams that are interested in you, but you can almost choose where you feel the most comfortable. That's something that was a big thing for me. It seemed like a natural fit talking to management and coaches."
Selected by Columbus in the fifth round (No. 127) of the 2008 NHL Draft, Calvert has 149 points (72 goals, 77 assists) in 416 NHL games and 10 points (six goals, four assists) in 16 playoff games.
"I've always liked Matt Calvert," Avalanche general manager Joe Sakic said. "With the departure of Blake Comeau (signed three-year contract with the Dallas Stars) we thought Matt would be a great fit to come in. He's 28, I know our coaching staff knows him really well. For 28 he's experienced, he plays hard, he plays fast, he brings energy, brings leadership. He can play up and down your lineup.
"Blake was a great leader in the dressing room and brought that energy and leadership on the ice, and Matt's going to do that as well for us. We're excited to have him and speaking with him this is a place where he really wanted to come."