Source told ESPN.com's Brian Windhorst that Brand received a one-year contract worth $4 million.
"Elton brings a veteran presence both on and off the court and is a welcomed addition to our locker room," Hawks president of basketball operations Danny Ferry said in a statement. "His ability to play center or power forward will give our frontcourt a great deal of versatility and we think he will be an outstanding fit to our program."
Last season for the Dallas Mavericks, the 34-year-old averaged 7.2 points, 6.0 rebounds and 1.3 blocks in 21 minutes per game.
The two-time All-Star has averaged 17.4 points, 9.1 rebounds and 1.8 blocks in his 14-year career.
Dallas, meanwhile, continues to pursue free-agent center Greg Oden while also negotiating with Milwaukee Bucks free-agent big man Samuel Dalembert, sources told ESPN.com's Marc Stein. The Mavericks were scheduled to meet with Oden on Monday in Las Vegas.
Information from ESPN.com's Marc Stein and Brian Windhorst and The Associated Press was used in this report.