Smith, 30, spent last season with the Orlando Magic, where he averaged 7.2 points and 2.9 rebounds per game in 76 games in what almost exclusively was a reserve role.
A jump-shooting 7-footer, Smith will give the Wizards further depth in their front court after Washington signed Ian Mahinmi and Andrew Nicholson over the weekend to fill in behind incumbent starters Marcin Gortat and Markieff Morris.
Including Smith, the Wizards now have 11 players either under contract or having agreed to contracts for next season, and they have used up virtually all of their cap space. To fill out the rest of the roster, they'll have the room exception, worth about $2.9 million and which can be given out on a two-year deal and veteran's minimum contracts.
Washington will likely pursue an extra wing with the room exception, giving them further depth behind Bradley Beal, Otto Porter Jr. and Kelly Oubre Jr. The Wizards traded for Trey Burke to back up John Wall and signed 6-foot-7 guard Tomas Satoransky, a second-round pick in 2012, who can fill in at both guard spots.