Weatherford will receive a five-year contract worth $12.75 million, ProFootballTalk.com reported.
"I'm looking forward to representing the NEW YORK GIANTS for the next 5 years. @giants thank you to our fans for making it an easy decision!" Weatherford tweeted.
The Giants needed time to negotiate the deal with Weatherford, who received the franchise tag prior to the start of free agency.
Weatherford was a crucial contributor to the Giants' run to winning Super Bowl XLVI. He stabilized the punting game and was clutch as well, averaging 45.7 yards per punt with a net average of 39.2 last season, and landed 25 punts inside the 20.
With Weatherford's help, the Giants improved their punting game and coverage after struggling in 2010. They have re-signed two of their key players in cornerback Terrell Thomas and Weatherford, and still hope to re-sign middle linebacker Jonathan Goff.