The signing is for the league minimum, sources confirmed to ESPN.com.
Lewis, a 16-year NBA veteran, played in 60 games for the Miami Heat this past season, averaging 4.5 points on 41.5 percent shooting from the field and 34.3 percent from 3-point range in 16.2 minutes per game.
His numbers increased en route to Miami's run to the NBA Finals, as he averaged 5.3 points on 41.2 percent shooting and 37.3 percent from long range in 17.7 minutes per game in the playoffs.
Lewis is stretch-4 who is a low-risk investment backup for Dirk Nowitzki. Based on his minutes from last season, the Mavs won't ask more, if that much, in terms of minutes.
Lewis is expected to join forward Richard Jefferson, who also is expected to sign for the league minimum, as reinforcements who can boost Dallas' perimeter shooting.
The Mavs still have their $2.7 million exception to use as well.
With the acquisition of Lewis, the Mavs have two roster spaces left. Sources have said the Mavs expected to re-sign Bernard James, who is currently without a contract and playing in the Las Vegas Summer League.
Information from ESPN.com's Marc Stein and ESPNDallas.com's Tim MacMahon was used in this report.