The one-year deal is worth $3 million and is totally guaranteed, sources said.
Burress, who will turn 34 in August, was released from prison in June after spending nearly two years in jail on a weapon possession charge.
Burress caught the winning touchdown in the 2008 Super Bowl as the Giants stunned the Patriots, dealing New England its only loss that season. Nine months later, his unlicensed handgun accidentally went off in a Manhattan nightclub, striking his thigh. The gun was not licensed in New York or in New Jersey, where Burress lived. His license to carry a concealed weapon in Florida had expired in May 2008.
Burress is on parole for two years. He has to get and keep a job, undergo substance abuse testing, obey any curfew established by his Florida parole officer, support his family and undergo any anger counseling or other conditions required by his parole officer.
Selected eighth overall in the 2000 draft, he has 505 receptions for 7,845 yards and 55 touchdowns in nine seasons.
Information from The Associated Press was used in this report.