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 in a statement. "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, all with Chicago, Brouwer has recorded 103 points (49 goals, 54 assists).
"He's a power forward who can get us 20 goals a year and play physical," Caps GM George McPhee said. "He just won a Stanley Cup a year ago. He's supposed to be a real good leader. So we're delighted to be able to add him to our lineup."
The trade provided Chicago with two first-round picks Friday night (No. 18 and No. 26). The Hawks took Mark McNeill, a forward with Prince Albert of the Western Hockey League, with the 18th pick and selected another forward, Philip Danault, from Victoria of the Quebec League, with the pick they acquired from Washington.
The emergence of rookie forward Ben Smith helped make Brouwer expendable. Smith, who joined the Hawks late in the regular season, scored 3 goals in the playoffs, including the overtime game-winner in Game 6 against Vancouver.
"We wish him well, he has certainly been a good Blackhawk," General Manager Stan Bowman said. "But we're excited. We added a first-round pick, and I think it is not easy to do that these days because of the way they are valued around the League.
Troy is a very good NHL player and a good member of our team, but there always comes a time when you need to open up spots for some of your younger players. ... It's tough to see a person like Troy go. He's been a great Blackhawk and he's a classy guy, a hard worker, and we are going to miss him.
Unless they make another deal, the Caps' first choice in the draft will now come at No. 117, late in the fourth round on Saturday. The Caps traded their second-round choice and their third-round pick in separate deals for defensemen Joe Corvo (to Carolina in 2010) and Dennis Wideman (to Florida in 2011).
It's the first time since 2001 that the Caps have not had a first-round pick.