Andersen holds the NFL record with 37 field goals of 50 yards or more. His 28 game-deciding kicks is also a league record.
Last year, Andersen made 25-of-31 FGs (80.6 percent), but Atlanta chose not to re-sign him.
On Wednesday, the Giants looked at three kickers: Andersen, Brad Daluiso, the second-leading scorer in Giants history, and Steve Videtich, a former kicker at North Carolina State.
The 41-year-old Andersen supplants 38-year-old Lomas Brown as the Giants oldest player.
"He obviously showed me that he still has the leg to do what we want," Head Coach Jim Fassel said. "I have a lot of respect for what he can accomplish in this league and what he can still accomplish. He's a true professional. I definitely think he brings a level of maturity and experience and success to that position.
"One of the things that he told me was that he wanted to be here because he wanted to be with a team that had a chance to go back to the Super Bowl. That's the most important thing to him."
Andersen is in his 19th season after being selected in the fourth round of the 1982 Draft by the Saints. The Denmark native played college ball at Michigan State.
"I'm very excited to be here," Andersen said. "This is a storied franchise with a lot of history. A lot of great players have come through here. I have a tremendous amount of respect for the Mara family and I'm excited to be a part of the organization."