The team confirmed the move Monday.
"I'm super excited to know that I will be with the Giants for at least one more season," Weatherford told the team's website. "I think the franchise tag is a step that needed to be taken to continue to work together on a long-term deal. I want to be with the Giants for a long time and I really think the feeling is mutual, so hopefully something can get worked out long term and I can be a Giant for another four, five or 10 years."
The Giants' decision to keep Weatherford over former seventh-round pick Matt Dodge last September turned out to be one of general manager Jerry Reese's best decisions as the punting game became a consistent weapon for New York.
During the Super Bowl XLVI win over the Patriots, Weatherford landed three of his four punts inside the 10 and the one that bounced into the end zone could have been downed near the goal line.
He is one of 20 unrestricted free agents on the Giants' roster. The team re-signed wide receiver Domenik Hixon last Friday.
Weatherford will be paid roughly $2.5 million, the average of the top five salaries at the position. If he signs with another team, New York will get two first-round draft picks.
Ohm Youngmisuk covers the Giants for ESPNNewYork.com. Information from The Associated Press contributed to this report.