According to ESPN, Tuck will sign the one-day contract with the Giants on Friday.
The 33-year-old Tuck announced in February that he was retiring after 11 NFL seasons. Tuck spent the last two years with the Oakland Raiders after playing for the Giants from 2005 to 2013.
Tuck won two Super Bowl rings with the Giants.
"After months of praying and careful consideration, I have decided to retire from the game of football," Tuck wrote in his Facebook post at the time. "I've had 11 great years and honestly I leave with very few regrets."
Tuck, who played just five games for the Raiders in 2015 due to a torn pectoral muscle, recorded 66.5 career sacks and had 10 or more in a season on four occasions. Tuck added 5.5 postseason sacks.