The 28-year-old forward had 33 points (14 goals, 19 assists) in 75 games with the Arizona Coyotes last season.
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"It's a great team and a great organization," Panik said of the Capitals. "They're always in the [Stanley Cup Playoffs] and it's a good opportunity for me. Hopefully I will be helping the team doing the best way I can.
"I think I can play everything. It just depends where I'm going to fit. I can play on the third line, fourth line, first line, it doesn't matter. I just want to be the difference guy and make the team better. We will see where I'm going to end up."
Last week, Washington traded forward Andre Burakovsky to the Colorado Avalanche.
Selected by the Tampa Bay Lightning in the second round (No. 52) of the 2009 NHL Draft, Panik has 159 points (75 goals, 84 assists) in 410 regular-season games with the Lightning, Toronto Maple Leafs, Chicago Blackhawks and Coyotes. He has four assists in 12 playoff games with Tampa Bay and Chicago.