NFL Network's Ian Rapoport reports the deal is a two-year contract worth $6.9 million, with $2.95 million guaranteed.
Stewart, 30, will be reunited with his former offensive coordinator, Mike Shula, who was hired by New York this offseason, and former Panthers general manager Dave Gettleman, who signed on to run the Giants in December.
"I am very pleased that we were able to make Jonathan a New York Football Giant," Gettleman said in a statement. "He is a quality runner with power and speed and brings a veteran, professional presence to our locker room. He’s a terrific addition for us at this time."
The former Pro Bowl running back ran for 680 yards and six touchdowns across 15 games in 2017. The yardage was Stewart's lowest output of any season in which he played at least 10 games. However, he still left the Panthers as the franchise's all-time leader in rushing yards (7,318).