Entering his 16th NFL season, Feagles played the previous five years for the Seattle Seahawks, after earlier stints with the New England Patriots (1988-89), Philadelphia Eagles (1990-93) and Arizona Cardinals (1994-97).
Jim Fassel worked with Feagles when he was the Cardinals offensive coordinator in 1996.
"He is, without a doubt, the best punter at placing the ball inside the 20,"Fassel said. "With what he can do there, his experience and his directional kicking, he may be the best punter in the league.
Last season with the Seahawks, Feagles punted 61 times and was fifth in the NFC (sixth in the NFL) with a 37.0-yard net punting average. His gross average was 41.7 yards. Last year, the Giants used rookie punter Matt Allen, who had a 36.9-yard gross average and a 32.5-yard net average.