Quincey, 31, had 15 points (six goals, nine assists) in 73 games with the Columbus Blue Jackets and New Jersey Devils last season.
"I pay a lot of attention to [my] defense," Quincey said. "I take a lot of pride in killing penalties and shutting down other teams top lines."
After signing a one-year contract with the Devils on Sept. 28, he was traded to the Blue Jackets on March 1.
Selected by the Detroit Red Wings in the fourth round (No. 132) of the 2003 NHL Draft, Quincey has 155 points (36 goals, 119 assists) in 568 games with the Blue Jackets, Devils, Red Wings, Colorado Avalanche and Los Angeles Kings.
Quincey was a reserve for the Red Wings when they won the Stanley Cup in 2008.
"I don't count that as winning the Cup," Quincey said. "I'm starving for my first Cup as a player, playing in that final game and being a huge part of it. That's where my drive is coming from right now and I think Minnesota has a great opportunity if we do what we should do and realize our potential."
