Terms were not disclosed, but an ESPN report said Burress received $25 million over six years.
The 6-5, 226-pound Burress was the eighth overall draft pick in 2000 by Pittsburgh and played five years with the Steelers, catching 262 passes and scoring 22 touchdowns.
"He makes us a better football team, there's no doubt about that," Coach Tom Coughlin said on the team's Web site. "He is a guy who has an imposing physical presence. And because he does have the ability to be a long-ball threat, he is a guy that will force defenses to pay particular attention to where he is."
Burress will fill the void created by the release of Ike Hilliard.