The 33-year-old wide receiver was taken 12th overall by the Giants in the 2014 NFL Draft and spent five seasons with New York before being traded to the Cleveland Browns in 2019.
Beckham made 390 catches for 5,476 yards and 44 touchdowns over 59 games for the Giants.
The Browns released Beckham in November 2021, and he signed with the Rams three days later. Beckham scored five touchdowns in eight regular-season games and two more in the playoffs, including a 17-yard touchdown catch in the Super Bowl as the Rams beat the Cincinnati Bengals for the title.
Beckham missed the 2022 season with a torn knee ligament suffered in the Super Bowl, then returned with the Baltimore Ravens in 2023 and played for the Miami Dolphins in 2024.
Beckham sat out last season, during which he was issued a six-game ban for violating the NFL's performance-enhancing drug policy.
He worked out for the Giants in April and again on Monday before signing with the club.
Overall, Beckham has 575 catches for 7,987 yards and 59 touchdowns, plus 23 rushes for 170 yards and a touchdown.