It's a three-year deal worth $12.5 million, although the third year is not guaranteed.
Brewer, 25, began last season with the Utah Jazz before being dealt to the Memphis Grizzlies near the trade deadline. He played five games with the Grizzlies before suffering a season-ending hamstring injury.
"I think the Bulls are a great fit for him," Brewer's agent, Henry Thomas, said in a phone interview.
Thomas noted that Brewer chose the Bulls over several other teams including the Celtics because of the fact that he has the opportunity to start right away and play with Derrick Rose as well as former teammates Kyle Korver and Carlos Boozer.
"He's excited about the opportunity," Thomas said.
Brewer didn't get a chance to bring the ball up the floor much in Utah because he played with former Illinois star Deron Williams, but Thomas believes that if Rose ever needs a breather, Brewer wouldn't have any problems handling the ball.
"He's definitely capable," Thomas said, noting that Bulls GM Gar Forman scouted Brewer while he was at Arkansas, playing a type of "point-forward" role.
Brewer's defensive prowess is one of the major reasons Forman decided to lock him up, and Thomas is confident that his client's skills will impress new Bulls head coach Tom Thibodeau.
He averaged nine points and three rebounds last season after averaging 13.7 points during the 2008-09 season.
Nick Friedell covers the Bulls for ESPNChicago.com.