"Hunter has agreed to terms with the Redskins," Thomas Mills, Smith's agent, wrote Thursday in an e-mail to The Associated Press.
Mills wouldn't release financial details of the one-year deal at Smith's request.
KTEN-TV in Denison, Texas, first reported the move. Smith is from Sherman, Texas, about 60 miles north of Dallas, and was visiting there this week.
Smith never missed a game in 10 years in Indianapolis, but he became a free agent after last season, and the Colts didn't re-sign him.
Smith has averaged 43.4 yards per punt in his NFL career. He averaged 44.2 yards last season, and his 38.8 net yards per punt last season was the highest total of his career.
The Redskins ranked last in the NFL in net punting average last season. Draft pick Durant Brooks won the job over incumbent Derrick Frost during training camp, then was cut and replaced by Ryan Plackemeier in October. Plackemeier was released in February.
The Redskins have signed two other punters this offseason, veteran Dirk Johnson and first-year player Zac Atterberry.
Copyright 2009 by The Associated Press