Wolski, 26, had four goals and eight assists for 12 points in 31 games with the New York Rangers and Florida Panthers in 2011-12. He was acquired by Florida from New York on Feb. 25, 2012, in exchange for defenseman Mike Vernace and a third-round selection in the 2013 NHL Draft.
"I definitely think I can help on the offensive side," Wolski said on a conference call with reporters, according to The Washington Times. "I struggled the last two years. I'm definitely highly motivated, very excited and very hungry at this point in time and I look forward to the opportunity to be able to play with great players. I think it's going to be a very positive year."
Wolski was selected by Colorado in the first round (No. 21) of the 2004 NHL Draft.
He registered career highs in goals (23), assists (42) points (65) and games played (80) and tallied four goals and one assist in seven playoff games during the 2009-10 season with Colorado and Phoenix. In 29 career playoff games, Wolski has eight goals and nine assists for 17 points.
The Zabrze, Poland, native participated in the 2007 NHL YoungStars game with new Capitals teammate Mike Green.
The Capitals also announced Wednesday they have re-signed center Zach Hamill, who played 16 games for the Boston Bruins last season. He was acquired in a trade for Chris Bourque on May 26.
Hamill had eight goals and 13 assists in 41 games for the Providence Bruins of the American Hockey League in 2011-12.