Smith, 31, a 10-year veteran, signed a one-year contract, the financial details of which were not yet available. Despite his long tenure with the team, Indianapolis did not seek to re-sign Smith when he became a free agent.
The former Notre Dame standout is the third punter, and the second veteran at the position, signed by the Redskins this offseason.
Washington ranked dead last in the league in 2008 in net punting average (33.4 yards) and had one punt blocked. The Redskins allowed two punt returns for touchdowns, the second-most in the league.
The Redskins began the 2008 season with rookie Durant Brooks as the punter. He was replaced late in the season by two-year veteran Ryan Plackemeier, who was released earlier this spring.
The Redskins signed free agent Dirk Johnson, who most recently punted four years for the Philadelphia Eagles, this spring. The team also added Zac Atterberry, a one-year veteran with no regular-season experience.
In his 10 seasons in Indianapolis, Smith averaged 43.4 yards gross and 35.5 yards net. Never noted as a directional punter and a player who often outkicked his coverage, Smith nonetheless had 193 punts inside the 20-yard line and just 61 touchbacks.
Last season, he averaged 44.2 yards gross and had a net average of 38.8 yards.
Smith was originally chosen by the Colts as seventh-round pick in the 1998 draft.
Len Pasquarelli is a senior NFL writer for ESPN.com.