Brouwer, who turns 26 in August, had 17 goals and 19 assists in 79 games for Chicago in 2010-11. He went 4-4-8 in 19 playoff games last year and helped the Blackhawks win their first Stanley Cup since 1961.
"I'm very excited to join the Washington Capitals organization," Brouwer said. "They are consistently one of the top teams in the NHL and I look forward to helping them reach the ultimate goal of winning the Stanley Cup."
During the 2009-10 season, Brouwer registered a career-high 22 goals and 40 points in 69 games with the Blackhawks. In 238 career NHL games with Chicago, Brouwer has recorded 103 points (49 goals, 54 assists).
The trade provided Chicago with two first-round picks Friday night (No. 18 and No. 26).