Smith, who's from Sherman, Texas, told KTEN-TV that he's looking forward to joining the Redskins and the chance to return to the Dallas area to play the Cowboys.
Smith, who's spent the past decade with Indianapolis, declined to disclose further details about his plan to join the Redskins.
Smith said he was in his hometown this week, about 60 miles north of Dallas, to play a benefit concert Saturday night, at Austin College, with his acoustic rock band.
In March, the Skins signed punter Dirk Johnson.
Washington ranked last in the NFL in net punting yardage average last season.